1ft STI 

.S3 




/I 



fXi 



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V 



1 If E 



Surveyor's Companion. 




WILLIAM SCHMOLZ, 

Mathematical Instrument Maker. 




8 i.v / n.i M ist r>, CJIi.: 

1882. 



• 




V 



A. KEY 



SOLAR REFLECTOR; 



WITH A NEW SET OF 



PRACTICAL TABLES, k. 



USEFUL IN 



SURVEYING, ENGINEERING, &c. 



By Wm. SCHMOLZ, 

SURVEYING-INSTRUMENT MAKER. 



i 
SAX FRANCISCO, CAL. 

1882. 



Entered according to Act of Congress, in the year 1881, 

By W. Schmolz, 
In the office of the Librarian of Congress, at Washington. 



T4f7? 

■S3 



P R E F ACE. 



The many complaints of surveyors, who night after night failed 
to observe Polaris, on account of clouds passing over the star, and 
the frequent request to devise an easy, practical method for the 
accurate determination of the meridian with a transit instrument \ 
during the day-time, led the undersigned to invent a "Solar Re- 
flector," which consists of a simple attachment to the telescope of ( 
a surveyor's transit instrument, enabling the operator to find, the 
tnie meridian by two equal altitudes of the sun. 

The telescope of a transit is, in construction, the same as a solar 
microscope : the sun's rays are received by the object-glass, and the 
received light proceeds in the true optical axis ; at the end of this 
mathematical line, and in the extension of the direct focus of the 
telescope lenses, there is the reflector placed to receive the image 
of the sun. 

For the purpose of making practical use of the sun's image on 
the reflector, tables of correction were calculated by W.J. Lewis, 
C. E. These tables will be good as long as the sun shines. To make 
the book more interesting, the most important parts of the "Sur- 
eyor's and Engineer's Companion," published in 1859 by Win. 
Schmolz, calculated by Dr. R. C. Matthewson, W. J. Lewis, C. E.. 
and G. F. Allardt, C. E. — are republished, with the addition of ' 
some new and original tables. 

The calculations have been made with great care ; every precau- 
tion has been taken to avoid typographical errors, by comparing 
the revised sheets with the original computations or the best au- 
thorities ; and it is firmly believed tnat the Rules and Tables will 
give accurate results. 



W, SCHMOLZ. 



Sam Fkanoisoo, Nov. 1, 1881. 



Ill 



INDEX. 



PAGE 

Schmolz's Patent Solar Reflector Description 5 

" " " ' Instructions 6 

" «• " '• Directions 7 

Ephemeris of the Sun, January and February 8 

" " *' Marcii and April 9 

" " " May and June 10 

" " " July and August 11 

" u " September and October 12 

u " u November and December 13 

Burt's Solar Compa>s , 14 

Meridian Distances West from Greenwich 14 

Fifty Principal Fixed Stars . . . 15 

Refraction in Declination for Solar Instruments 16 

Increase or Decrease of the Sun's Declination 17 

,; Solar Transit ' — Schmolz's Invention 18 

Description of Schmolz's Solar Transit 19 

Azimuths of Polaris, from 1881 to 1900 20 

Eastern and Western Elongation of Polaris 21 

Explanation and Use of the Table I 22 

Explanation and Use of Tables II and III 23 

Length of a Degree of Latitude from 29° to 38° 24 

»« " 4 " 4t " 39°to48o 25 

Length of a Degree of Longitude from 29° to 38° 26 

" " " " " 39° to 48° 27 

Divergency of the Parallel of Latitude, &c 28 

Difference of Latitude and Departure, &c 28 

Reducing Feet to Chains and Chains to Feet 29 

Tables of Acres Required per Mile, for Different Widths. . 29 

Miscellaneous Rules ". . 30 

11 31 

Principal Lines of the U. S. Surveys in California 32 

" " u Nevada,... 33 

" kt u " " " Utah 33 

" Arizona 34 

lt " " " " "Montana 34 

" " " " " "Washington, 34 

'« "Oregon 35 

Acknowledgements to the Hon. U. S. Surveyor-Generals. 35 

Tables of Grades. 36 

Table of Radii, Middle Ordinates and Curves 37 

Temp?rature of Boiling Water for Different Altitudes. ... 38 

Thermometers — Fahrenheit, Centigrade, and Reaumur. ... 39 

Equivalent of Measures 40 

Equivalent of French Measures and Weights 41 

U. S. Gold and Silver Coins 42 

Value of Gold and Silver, of Different Fineness 43 

A Card 44 



IT 



hESORirTK I 

SCII M () LZ*S P A T E N T S I. A U li K V L E T R. 




Fig I represents the complete attachment. A is a slide, which fits in a dove- j 

tailed groove in the eye-piece cap. B is a double-bent piece of brass, firmly fastened ( 

to A with two screws. On the inside of B is a graduated silver plate, standing at ( 

1 right angle to the optical axis ; the graduation on the silver plate corresponds to the { 

diameter of the sun's image. 

Fig. 2. The reflector is in position for the observation. 

Fig. 3 represents the object-glass cap, with a small hole in the center, for the pur- 
pose of reducing the sun's diameter and also its bright, strong, glaring light. The ad- 
vantage gained by the object-glass diaphragm is very decided ; it gives a soft, 
i sharp edge to the image of the sun on the reflector, and prevents injury to the eye- } 
1 sight, as no direct sight at the sun through the telescope is required in taking the 
1 double equal altitudes. 

The method of finding the true meridian by two equal altitudes of the sun is no < 
new discovery. The Hindoos, Egyptians, Greeks, Arabs, were early acquainted with i 
it, and by tnc Romans it was employed in laying out cities. Surveyors familiar with I 
the modern computations very seldom use it, on account of the tedious, complicated ' 
formulas which are found in Bowditoh, page 162; Weissbaeh, page 322 ; and those un- 
, acquainted with the solution of the problem we refer to the May number, 1S7S, of * 
the "Engineer of the Pacific." 

The advantage of the reflector consists principally in the simple, practical way with 

which a correct scientific result is obtained. It does not require cross-hair calculation 

1 for sun's center-passage, equation of time, elapse of time and co-latitude, zenith dis 

tancc, azimuth of the sun, error of the collimation, inclination of axis, deviation of / 
' instrument in azimuth, difference in longitude, parallax, refraction, Greenwich time, 
1 apparent, solar, sidereal and mean time, logarithms, correction for chronometer rate, i 
1 correction for inequality of level and axis, and, finallv and principally, the errors of ( 
calculation. 

The little magical reflector can be attached to any transit instrument, which is pro- 
vided with a chini]> and tangent screw for the telescope axis. 
In desiring to have a solar reflector fitted to a transit, the owner has not to send the ' 
! complete instrument. All that is required is the cap of the eye-piece and the cap of ) 
, the object-glass. 

By following the annexed instructions, every practical surveyor can convince him- i 
I self of the accuracy of the assertion that the solar reflector gives a satisfactory result; < 
i and any expert will find that a true meridian line established by this method will < 
• critical examination within Ave seconds of arc. 



INSTRUCTIONS. 

to determine the ti1de meridian by two equal altitudes of the 

Sun, with "Schvolz's Patent Solar Reflector." 



ZEXETH 



// ! \ s 


[ i 


POLARIS ^S X 

s /I NX 

§ / \\ 


U^^^T^! 1 / 


> 


^-^__\ 





Set up the transit instrument at the place of observation, P ; see that there U no I 
i dead motion in the tangent-screws and tripod-legs ; slide the Solar Keflector into the I 
i eye-piece cap ; put the cover with the small hole over the object-glass ; clamp the I 
i vernier of the horizontal plate to zero ; then level up the instrument, turn it on the ( 
lower pla te center toward the sun, and raise the telescope till the sun's image appears * 
1 on the reflc-ctor. Clamp the telescope axis and the lower plate center, and bring with 
1 the vertical axis tangent screw and with the lower plate tangent screw the image of > 
the sun exactly within the graduated lines of the reflector. Kote the time, and make ( 
it so that the forenoon observation will correspond nearly in time with one of the col- < 
umns of the correction table. Be careful that the position of the instrument is not ( 
) disturbed* and that the vernier of the horizontal plate remains at zero ; because zero 
i is the starting-point for the afternoon observation. 

The afternoon observation will be sooner or later, as the case may be, on account ' 
i of the declination of the sun ; and it is important that the observer should be aware of S 
» this, so that he may not put any reliance on exact corresponding meridian distance as 
1 to time for the afternoon observation, The second observation, or the double-equal 
1 altitude of the sun, is fast or slow : but the observer must not lose confidence in the ( 
1 accuracy of his established true meridian line on account of this irregularity, as the 
* table will afterwards make the necessary correction. Taking it for granted that the ( 
1 instrument has remained undisturbed in the same position during the time since the < 
forenoon observation was taken, and as the time for the afternoon equal altitude of the I 
sun is approaching, the observer has to loosen carefully the horizontal vernier t 
) clamp, and slowly turn the instrument on the horizontal circle in the direction the I 
i sun has moved. As soon as the sun's image begins to appear on the reflector, the < 
i observer has to fasten the clamp of the horizontal vernier, and make the final motion ( 
i with the horizontal vernier tangent screw alone. The utmost precaution has to be 
i taken not to move the lower clamp and tangent-screw, or the telescope axis tangent ) 
i screw, as any motion on either ot those parts will make the observation worthless. 

The sun is moving very fast; two seconds of time can be distinctly seen on the i 
I reflector* the observer must therefore be very attentive and quick : he must follow < 

with the horizontal vernier tangent screw the oblique course of the sun on the re- 
1 flector till the image is precisely in the same place between the graduated lines as by 
► tbe former observation. When this is satisfactorily done, then the observer lias to find ( 
) correctly the horizontal anscle. and make the necessarv corrections for the true me- | 
i ridian line, as shown hereafter. 



D I R E T I N s 
For the Use of the Table of Corrections. 



Find in the ephemeris of the sun the hourly difference of the sun's declination in ( 
' seconds, for the date of observation; and find in the correction table the number < 
which corresponds to the latitude of the place and to the time of morning obcerva- ( 
tion, multiply the number In the correction-table with the hourly difference of the 
I sun's declination, and the product will be the correction in minutes of arc. 

The actual or abstract multiplier to give the result in seconds of arc is sixty times I 
the number given in the table below j but we have divided by sixty, so as to give I 
minutes of arc at once, as not less than a minute of arc can be read on the division o( ( 
a transit instrument. 

Between Dec. 22d and June 22d the sun is moving North, or the north polar dis- 
tance is decreasing, and the correction found by the multiplier must be subtracted ( 
i from the angle as found on the horizontal plate between the fore and afternoon ob- < 
servations, and the line bisecting the remaining angle will be the true meridian. But ' 
1 between June S2d and Dec .22(3, when the sun is moving South or the north polar dis- 
1 tance is increasing, add the correction to the horizontal angle, as found in the read- 
ing of the instrument, and the line bisecting the sum of these two angles will be the ' 
true meridian. 

TABLE OF CORRECTIONS. 



Lat. 


8 


8k 


9 


9h 


10 


10* 


11 


11* 




A. If. 

0.18 


A. M. 

0.17 


A. M. 


A. M. 


A. M. 


A. M. 


A .M. 


A. M. 


82° 


0.17 


0.16 


0.16 


0.15 


0.15 


0.14 


33° 


0.18 


0.18 


0.17 


0.16 


0.16 


0.16 


0.15 


0.15 


34° 


0.19 


0.18 


0.17 


0-17 


0.16 


0.16 


0.16 


0.15 


35° 


0.19 


0.18 


0.17 


0.17 


0.16 


0.16 


0.16 


0.15 


36° 


0.19 


0-18 


0.17 


0.17 


0.16 


0.16 


0.16 


0.15 


37° 


0-19 


0.18 


0.18 


0.17 


0.17 


0.16 


0.16 


0.16 


38P 


0.20 


0.19 


0.18 


0.17 


0.17 


0.17 


0.16 


0.16 


39° 


0.20 


0.19 


0.18 


0.18 


0.17 


0.17 


0.17 


0.16 


40° 


0.20 


0.19 


0.18 


0.18 


0.17 


0.17 


0-17 


0.16 


41° 


0.20 


0.19 


0.19 


0.18 


0.18 


0.17 


0.17 


0.17 


42° 


0.21 


0.20 


0.19 


0.18 


0.18 


0.18 


0-17 


0.17 


430 


0.21 


0.20 


0.19 


0.19 


0.18 


0.18 


0.18 


0.17 


440 


0.21 


0.20 


0.20 


0.19 


0.19 


0.18 


0.18 


0.18 


45° 


0.22 


0.21 


0.20 


0.19 


0.19 


0.18 


0.18 


0.18 


46° 


0.22 


0.21 


0.20 


0.20 


0.19 


0.19 


0.19 


0.18 


47° 


0.23 


0.22 


0.21 


0.20 


0.20 


0.19 


0.19 


0.19 


48° 


0.23 


0.22 


0.21 


0.20 


0.20 


0.20 


0.19 


0.19 


49 ■ 


0.23 


0.22 


0.22 


0.21 


0.20 


0.20 


0.23 


0.19 



g^jfSuostract 

the product 

of the 

multiplication 

between . 

December 22d 

and June 22d. 



|^T* Add the 

product of the ( 
multiplication , 

between 

June 22d and \ 

Dec. 22d. ) 



Example I. May 24th, 1881, 8:30 a.m., at San Francisco, in lat. 37 deg. 48min. 1 
north, I took the altitude of the sun's image ; and seven hours afterwards, at 3:30 p.m, < 
1 had the same altitude. The horizontal angle between the two observations mea- < 
1 sured 163 deg. 33 min., and the hourly differences in the sun's declination in the ephem- ' 
eris was 87-46 seconds. The tabular number for lat. 3Sdeg and 8:30 a.m. is 0.19 ; ( 
hence correction is : 2". 40 x 0.19 gives 5 minutes ; horizontal angle is 168 deg. 33 min., ( 
from which deduct 5 min., leaving 168 deg. 28 min., which divided by two gives ' 
-1 deg. 11 min. for the true meridian. 

Example II. Sept. 10th, 1SS1, at 11 o'clock a.m., at the same place of observa- I 
tion, the horizontal angle measured at 1 p.m. 53 deg 41 nun.; the hourly difference in < 
1 the sun's declination was 5G.9S seconds. The tabular number for 33 deg. and 11 A.M,is ' 
) 0.10; hence correction Is: 50. 9S x 0.10 gives 9 minutes; horizontal angle is 52 deg ( 
; 41 min., to which add 9 min., making 52 deg. 50 min., which divided by two gives 
' M ch'g 25 min. for the true meridian. / 

After establishing the line on the ground, the whole manipulation Is finished. \ 



TABLES 



EPHEMEKIS OF THE SUN. 



At Greenwich, mean Noon. 



JANUAEY, 1882. 


FEBRUARY, 1882. 

> 


Day 
of 
Mo. 


Apparent 
Declination, 


Diff. for 
1 Hour. 


Equation 
of time 
to be 
Added to 
Apparent 
Time. 


Apparent 
Declination. 

o / // 


Diff, for 
1 Hour. 


Equation ( 
of Time ( 
to be ( 
Added to ) 
Apparent ) 




o / // 


// 


m. s. 


// 


m. s. r 


1 
2 
3 


S. 22 59 37.6 
22 54 20.1 
£2 48 35.2 


+12.66 
13.81 
14.94 


3 53.49 

4 21.53 
4 49.19 


3. 17 2 12.5 
16 44 55.2 
16 27 20.5 


+42.83 
43.57 
44.30 


13 51.41 ; 

13 58.C5 ) 

14 5.06 S 


4 
5 

6 


22 42 23.1 
22 35 44.1 
22 28 38.1 


+16.07 
17.20 
18.31 


5 16.46 

5 43.S0 

6 9.71 


16 9 28.5 
15 51 10.9 
15 32 55.0 


+45.00 
45.70 
46.37 


14 10.66 ( 
14 15.45 ( 
14 19-43 ( 


7 
8 
9 


22 21 5.6 
22 13 6.6 
22 4 41.6 


+19.41 
20.50 
21.58 


6 35.64 

7 1.08 
7 2f.00 


15 14 14.1 
14 55 17.6 
14 36 6.1 


+47.04 
47.67 
48.28 


14 22.62 ( 
14 25.02 / 
14 26.66 ) 


10 

11 

> 12 


21 55 50.6 
21 46 33.9 
21 36 51.6 


+22.66 
23.73 
24.78 


7 50.38 

8 14.20 
8 37.45 


14 16 39.8 
13 56 59.3 
13 37 4.8 


+48.89 
49.48 
50.04 


14 27.53 ) 
14 27.63 ) 
14 26.98 ) 


) 13 

> 14 

> 15 


21 26 44.2 
21 16 12.0 
21 5 15.2 


+25.82 
26.85 
27.87 


9 0.09 
9 22.10 
9 43.47 


13 16 56.9 
12 56 36.0 
12 36 2.5 


+50.60 
51.13 
51.65 


14 25.61 ) 
14 2?.50 > 
14 20.66 \ 


! ie 

17 

18 


20 53 64.1 
20 42 9.2 
20 30 0.6 


+28.87 
29.85 
30.82 


10 4.19 
10 24.21 
10 43.51 j 


12 15 16.8 
11 54 19.6 
11 33 11.1 


+52.14 
5i>.62 
53.07 


14 17.11 ( 

14 12.85 < 
14 7.89 ( 


> 19 
) 20 
) 21 


20 17 28.9 
20 4 34.2 
19 51 17.1 


+31-79 
32.74 
33.67 


11 2.09 
11 19.93 
11 37.01 


11 11 51.7 
10 50 21.8 
10 28 42.0 


+53.53 
53.94 
54.36 


14 2.25 ( 
13 55.93 / 
13 48-95 ) 


) 22 
) 23 

) 24 


19 37 37.9 
19 23 3G.9 
19 9 14.4 


+34.59 
35.48 
36.37 


11 53.31 

12 8.82 
12 23.52 


10 6 52.8 
9 44 54.1 
9 22 46.8 


+54.74 
55.11 
55.47 


13 41-32 ) 

13 33.05 ) 
13 24.16 \ 


I 25 
> 26 
) 27 


18 54 31.0 
18 39 27.1 
18 24 3.0 


+37.23 
38-08 
38.91 


12 37.41 

12 50.48 

13 2.73 


9 31.3 
8 38 7.9 
8 15 37.0 


+55.81 
56.13 
56.44 


13 14.65 ( 
13 4.54 ( 
12 53.87 ( 


) 28 
) 29 
) 30 
) 31 


18 8 19.0 
17 52 15.6 
17 35 53.0 
17 19 11.8 


+39.74 
40.54 
41.33 
42.08 


13 14.14 

13 24.70 i 
13 34.43 ! 
13 43.34 [ 


7 52 58.9 
S. 7 30 14.1 


56.73 
+57.00 


12 42.63 ( 
12 30.84 \ 


I 32 


S. 17 2 12.5 


+42.83 


13 51.41 i 






} 



TABLES. 





EPHEMERIS OF THE SUN. 








At Greenwich, 


mean Noon. 






) MARCH, 1882. 


APRIL, 1882. 


Day 
( of 
)Mo. 


Apparent 
Declination, 


Diff. for 
1 Hour. 


Equation 
of time 
to be 
Added to 
Apparent 
Time. 


Apparent 
Declination. 


Diff, for 
1 Hour, 


Equation / 
ofTime ) 

to be v 

Attdi-d to ( 


Subtracted ( 

from ( 

Apparent / 

Time, ) 




o / // 


// 


m. s. 


o r // 


// 


m. s. ) 


j 1 
) 2 
) 3 


S. 7 30 14.1 
7 7 22.9 
6 44 25.7 


+57.00 
57.25 
57.49 


12 30.84 
12 18.55 
12 5.77 


N. 4 36 50.6 

4 59 54.8 

5 22 53.7 


+ 57.78 
57.57 
57.34 


3 54.05 ( 
3 35.90 ( 
3 17.87 ? 


I 4 
I 5 

I 6 


6 21 22.8 
5 58 14.7 
5 35 1.7 


+57.71 
57.93 
58.13 


11 52.50 
11 38.79 
11 24.65 


5 45 47.1 

6 8 34.4 
6 31 15.5 


+57.11 

56.85 
56.58 


2 59.99 ) 
2 42.27 ) 
2 24.75 ) 


7 
) 8 
) 9 


5 11 44.2 
4 48 22.5 
4 24 57.0 


+58.32 
58.48 
58.64 


11 10.10 
11 55.17 
10 39.88 


6 53 49.9 

7 16 17.4 
7 38 37.7 


+56.31 
56.00 
55.69 


2 7.45 ) 
1 50.39 ) 
1 33.59 ( 


) 10 
) 11 

t 12 


4 1 28.0 
3 37 55.9 
3 14 21.1 


+58.77 
58.89 
58.99 


10 24.25 
10 8.31 
9 52.09 


8 50.3 
8 22 54.9 
8 44 51.4 


+55.36 
55.03 
54.67 


1 17.07 I 
1 0.83 ( 
44.91 ( 


) 1S 
) 14 
( 15 


2 50 44.1 
2 27 5.1 
2 3 24.0 


+59.09 
59.15 
59.21 


9 35.59 
9 18.82 
9 1.81 


9 6 39.1 
9 28 17.8 
9 49 47.2 


+54.30 
53.91 
53.52 


29.30 ( 
14.03 ( 


0.89 I 


( 16 
( 17 

( 18 


1 39 42.9 
1 16 0.5 
52 17.8 


+59.24 
59.28 
59.28 


8 44.60 
8 27.21 
8 9.63 


10 11 6.8 
10 32 16.4 
10 53 15.6 


+53.11 
52.69 
52.24 


15.44 ( 
29.60 ( 
43.36 r 


I 19 
) 20 
) 21 


28 35.1 
S. 4 52.7 
fl. 18 49.0 


+59.28 
59.25 
59.21 


7 51.87 
7 33.96 
7 15.93 


11 14 4.1 
11 34 41.4 
11 55 7.3 


+ 51.78 
51.31 
50.83 


56.74 ) 

1 i>.7'2 ) 
1 22.29 ) 


) 22 
) 23 
S 24 


42 29.5 

1 6 8.5 
1 29 45.4 


+59.15 
59.09 
59.00 


6 57.79 
6 39.55 
6 21.23 


12 15 21.4 
12 35 23.4 
12 55 13.0 


+ 50.33 
49.81 
49.29 


1 34-42 ) 
1 46.10 \ 

1 57.33 ( 

2 8.11 
2 18.12 
2 28.26 


( 25 
( 20 
^ 27 


1 53 20.1 

2 1G 52.2 
2 40 21.4 


+58.90 
58.77 
58.65 


6 2.84 
5 44.40 
5 25.95 


13 14 49.8 
13 34 13.4 
13 53 23.6 


+48.76 
48.20 
47.63 


) 28 
) 20 
) 30 
S 31 

( 82 


3 3 47.3 
3 27 9.4 

3 50 27.5 

4 13 41.4 

N. 4 36 50.6 


+58.50 
58.35 
58.17 
57.98 

+57.78 


5 7.49 
4 49.05 
4 30.65 
4 12.31 

8 54.05 


14 12 20.1 
14 31 2.6 
14 49 30.8 

N.15 7 44.3 


+ 47.07 
46.48 
45.87 

+45.25 


2 BT.«1 

2 4C.47 ( 

3 168 

. J 



TABLES. 





EPHEMERIS OF THE SUN. 








At Greenwich, 


mean Noon. 






MAY, 1882. 


JUNE, 1882. < 


Day 
of 


Apparent 
Declination, 


Din", for 

1 Hour. 


Equation 

of time 

to be 

Subtracted 

from 

AppareHt 

Time. 


Apparent 
Declination. 


Diff, for 
1 Hour, 


Equation ( 

of Time ) 

to be ) 

Subtracted^ 

from ( 


Mo. 


"Added to ( 

Apparent ( 

Time, ; 


1 
2 
3 


o / // 

N.15 7 44.3 

15 25 42.9 

15 43 26.2 


// 

+45.25 
44.63 
43.98 


m. s. 
3 2.65 
3 9.94 
3 16.69 


o / // 

N.22 4 56.5 

22 12 51.1 

22 20 22.5 


// 

+20.26 
19.29 
18.32 


m. s. > 
2 27.67 i 
2 18.55 < 
2 9.04 < 


4 
5 
6 


16 54.0 
16 18 5.9 
16 35 1.7 


+43.32 
42.66 
41.99 


3 22.88 
3 28.50 
3 33.55 


22 27 30.5 
22 34 14.9 
22 40 35.6 


+17.34 
16.35 
15.36 


1 59.16 ) 
1 48.91 ( 
1 38.32 ) 


7 
8 
9 


16 51 41.1 

17 8 3.6 
17 24 9.1 


+41.29 

40.58 

♦ 39.87 


3 38.02 
3 41.91 
3 45.22 


22 46 3.32 
22 52 5.6 
22 57 14.5 


+14.37 
13.37 
12-36 


1 27.41 ) 
1 16.19 ; 
1 4.67 ) 


10 
11 
12 


17 39 57.1 

17 55 27.6 

18 10 40.2 


+39.14 
38.40 
37.64 


3 47.93 
3 50.03 
3 51.54 


23 1 59.2 
23 6 19.5 
23 10 15.4 


+11.35 
10.33 
9.31 


52.88 ) 
40.85 S 
28.59 S 


13 
14 


18 25 34.5 
18 40 10.3 


+36.88 
36.10 


3 52.46 
3 52.79 


23 13 46.9 
23 16 53.8 


+ 8.30 
7.27 


16.13 ( 
3.51 ( 


15 


18 54 27.1 


35.30 


3 52.53 


23 19 36.0 


6.24 


9.26 S 


16 
17 
18 


19 8 24.9 
19 22 3.2 
19 35 22.0 


+34.49 
33.68 
32.86 


3 51.70 
3 50.30 
3 48.33 


23 21 53.5 
23 23 46.4 
23 25 14.5 


+ 5.21 
4.18 
3.15 


22.15 S 
35.14 S 
48.20 ( 


19 

20 
21 


[19 48 20.7 
20 00 59.2 
20 13 17.1 


+32.02 
31.17 
30.32 


3 45.82 
3 42.77 
3 39.17 


23 26 17.8 
23 26 56.3 
23 27 10.0 


+ 2.12 

1.09 

+ 0.05 


1 1.28 C 
1 14.37 ( 
1 27.44 I 


22 

23 
24 


20 25 14.4 
20 36 53.7 
20 48 5.8 


+29.45 
28.56 
27.67 


3 35.04 
3 30.42 
3 25.31 


23 26 58.9 
23 26 23.0 
23 25 22.4 


- 0.98 
2.01 
3.04 


1 40.47 ) 

1 53.44 ) 

2 6.29 > 


) 25 

v 26 
> 27 


20 58 59.4 

21 9 31.5 
21 19 41.6 


+26.77 
25.87 
24.95 


3 19.70 
3 13.61 
3 7.06 


23 23 57.1 
23 22 7.1 
23 19 52.5 


- 4.07 
5.10 
6.12 


2 19.04 ) 
2 31.65 ) 
2 44.10 ) 


J 28 
29 
30 
31 

1 32 


21 29 29.6 
21 38 55.3 
21 47 58.4 
21 56 38.9 

N.22 4 56.5 


+24.03 
23.10 
22.16 
21.21 

+20.26 


3 0.06 
2 52.61 
2 44.72 
2 36.40 

2 27.67 


23 17 13.4 
23 14 9.8 
23 10 41-6 

N.23 6 49.0 


- 7.15 
8.17 
9.19 

-10.20 


2 56.37 I 

3 8.45 ( 
3 20.31 ( 

3 31.93 ? 



10 



TABLES. 



EPHEMERIS OF THE SUN. 






At Greenwich, 


mean Noon. 






JULY, 1882. 


AUGUST, 1882. 


►Day 

s of 


Apparent 
Declination, 


Diff. for 
1 Hour. 


Equation 
ot time 
. to be 
Added to 
Apparent 
Time. 


Apparent 
Declination. 


Diff. for 
1 Hour, 


Equation 

of'fime 

to be 

Added to 


Subtracted 

from 
Apparent 

Time. 




o / // 


// 


m. s. 


o / // 


// 


m. s. 


) 1 
) 2 
) 3 


N.23 6 49.0 
23 2 32.3 
22 57 51.4 


-10.20 
11.21 
12.21 


3 31.93 
3 43.30 
3 54.39 


N.17 59 46.8 
17 44 29.3 
17 28 54.4 


-37.86 
38.60 
39.31 


6 4.61 
6 0.67 
5 56.13 


) 4 
) 5 

) 6 


22 52 46.4 
22 47 17.5 
22 41 24.8 


-13.21 
14.20 
15.19 


4 5.19 
4 15.71 
4 25.90 


17 13 2.4 
16 56 53.5 
16 40 28.1 


-40.02 
40.71 
41.40 


5 51.00 
5 45.29 
5 39.01 


I 7 
8 
9 


22 35 8.4 
22 28 28.5 
22 21 25.3 


-16.17 
17.14 
18.11 


4 35.75 
4 45.25 
4* 54.38 


16 23 46.4 
16 6 48.8 
15 49 35.5 


-42.06 
42.72 
43.37 


5 32.14 
5 24.70 
5 16.70 


I 10 
C n 
) 12 


22 13 58.8 
22 6 9.2 
21 57 5C.9 


-19.08 
20.03 
20.97 


5 3.11 
5 11.42 
5 19.31 


15 32 7.1 
15 14 23.7 
14 56 25.6 


-44.00 
44.61 

45.22 


5 8.15 
4 59.03 
4 49.36 


) 13 
14 

( 15 


21 49 22.0 
21 40 24.7 
21 31 5.0 


-21.91 
22.84 

23.77 


5 26.70 
5 33.73 
5 40.22 


14 38 13.1 
14 19 46.7 
14 1 6.5 


-45.81 

46.39 
46.95 


4 39.14 ( 
4 28.38 < 
4 17.08 < 


S 16 
( 17 

s 18 


21 21 23.5 
21 11 20.2 
21 55.3 


- 24.68 
25.58 
26.47 


5 46.22 
5 51.71 
5 56.66 


13 42 12.9 
13 23 6.3 
13 3 47.1 


-47.51 
48.03 
48.55 


4 5.25 ( 
3 52.89 ( 
3 40.01 ( 


) 19 

) 20 

( 21 


20 50 9.0 
20 39 1.8 
20 27 33.9 


-27.35 
28.23 
29.09 


6 1.06 
6 4.90 
6 8.17 


12 44 15.5 
12 24 32.0 
12 4 36.8 


-49.05 
49.56 
50.04 


3 26.61 ( 
3 12.72 ( 
2 58.34 ( 


) 22 

) 23 

) 24 


20 15 45.5 
20 3 36.7 

19 51 7.9 


-29.94 
30.78 
31.61 


6 10.86 
6 12.96 
6 14.45 


11 44 30.1 
11 24 12.3 
11 3 43.8 


-50.51 
50.96 

51.41 


2 43.48 \ 
2 28.16 ) 
2 12.08 < 


< 25 
( 20 
( 27 


19 38 19.3 
19 25 11.1 
19 11 43.0 


-32.43 

^ 33.23 

34.03 


6 15.35 
6 15.64 
6 15.31 


10 43 4.9 
10 22 15.8 
10 1 16.8 


-51.84 
52.25 

52.66 


1 56.17 \ 
1 39.65 1 

1 2 -2. r> 2 v 


< 28 
/ 29 
( 30 

; 3i 

I 32 


18 57 57.2 
18 43 52.1 
18 29 28.5 

18 14 4C.G 

N.17 59 4C.8 


-34.81 

37.11 

-37.86 


6 14.38 
6 12.85 
6 10.71 
6 7.96 

fi 4.61 


9 40 8.3 
9 18 50.4 
8 57 2:<.5 
8 35 48.1 

N. 8 14 4. 4 


-53.05 
5:U3 
53.79 
54.15 

-54.49 


1 5.11 ) 

47.:'4 ) 
29.23 > 

10.80 ) 





11 



TABLES. 



EPHEMERIS OF THE SUN. 



At Greenwich mean Noon. 



SEPTEMBER, 1882. 


OCTOBEK, 1882. 


Day 
of 

Mo. 


Apparent 
Declination, 


Diff. for 
1 Hour. 


Equation 

or' time 

to be 

Subtracted 

from 

Apparent 

Time. 


Apparent 
Declination. 


Diff, for 
1 Hour, 


Equation 

of Time 

to be 

Subtracted 

from 

Apparent 

Time, 


1 
2 
3 


o / // 

N. 8 14 4.4 

7 52 12.7 

7 30 13.3 


// 

-54.49 
54.82 
55.14 


m 





s. 

7.93 . 
26.94 
46.21 


o / // 
S. 3 15 0.9 

3 38 17.7 

4 1 32.1 


// 

-58.23 
58.15 
58.05 


m. s. 
10 21.10 
10 40.09 
10 58.76 


4 
5 
6 


7 8 6.4 
6 45 52.5 
6 23 31.7 


-55.44 
55.73 
56.01 


1 
1 
1 


5.74 
25.50 
45.48 


4 24 43.9 

4 47 52.4 

5 10 57.5 


-57.92 
57.78 
57.63 


11 17.09 
11 35.04 
11 52.60 


7 
8 
9 


6 1 4.5 
5 38 31.2 
5 15 52.3 


-56.27 
56.51 

56.75 


2 
2 
2 


5.63 
25.95 
46.42 


5 33 58.6 

5 56 55.7 

• 6 19 48.2 


-57.46 

57.27 
57.08 


12 9.74 
12 26.45 
12 42.73 


> 10 

' 12 


4 53 7.9 
4 30 18.5 
4 7 24.4 


-56.96 
57.15 
57.34 


3 
3 
3 


7.03 
27.75 

48.58 


6 42 35.7 

7 5 17.9 
• 7 27 54.2 


-56.87 
56.64 
56.39 


12 58.55 

13 13.88 
13 28.72 


> 13 

> 14 

> 15 


3 44 26.0 
3 21 23.5 
2 58 17.4 


-57.52 

57.68 
57.82 


4 
4 
4 


9.50 
30.51 
51.57 


7 50 24.5 

8 12 48.1 
8 35 4.8 


-56.12 
55.83 
55.54 


13 43.05 

13 56.86 

14 10.14 


) 16 
) 17 
) 18 


2 35 7.9 
2 11 55.5 

1 48 40.4 


-57.96 
58.07 
58.17 


5 

5 

5 


12.68 
33.81 
54.95 


8 57 14.1 

9 19 15.8 
9 41 9.3 


-55.22 
54.89 
54.56 


14 22.86 
14 35.02 
14 46.60 


I 19 

? 20 
(J 21 


1 25 23.2 
1 2 4.0 
38 43.3 


-58.26 
58.33 
58.39 


6 
6 
6 


16.08 
37.19 
58.23 


10 2 54.3 
10 24 30.4 
10 45 57.2 


-54.19 

53.81 
53.42 


14 57.59 

15 7.95 
15 17.69 


22 
) 23 
) 24 


N. 15 21.2 

S. 8 1.8 

31 25.5 


-58.43 
58.47 
58.49 


7 
7 
8 


19.21 

40.09 
0.87 


11 7 14.3 
11 28 21.3 
11 49 18.0 


-53,00 
52.57 
52.13 


15 26.79 
15 35.23 
15 42.99 


) 25 

) 26 
) 27 


54 49.4 

1 18 13.4 
1 41 36.8 


-58.49 
58.49 
58.46 


8 
8 
9 


21.51 
41.99 
2.27 


12 10 3.8 
12 30 38.3 
12 51 1.3 


-51.67 
51.19 
50.71 


15 50.06 

15 56.41 

16 2.02 


\ 28 
S 29 
\ 30 


2 4 59.7 
2 28 21.5 
2 51 42.1 


-58.42 
58.37 
58.30 


9 
9 
10 


22.35 

42.20 

1.79 


13 11 12.4 
13 31 11.1 

13 50 57.0 

14 10 29.6 


-50.20 
49.68 
49.13 
48.57 


16 6.88 
16 10.98 
16 14.31 
16 16.85 


( 31 


S. 3 15 0.9 


-58.23 


10 


21.10 


S. 14 29 48.8 


-48.00 


16 18.58 



12 



T A u L K s . 



EPHEMEKIS OF T H ESUN 



AT GrKEBNWIOH MEAN NOON. 



NOVEMBER, 1882. 



Apparent 
Declination, 



S. 14 23 48.8 

14 18 54.0 

15 7 44.9 

15 26 20.9 

15 44 41.8 

16 2 46.9 

16 20 36.1 

16 38 8.9 

16 55 24.8 

17 12 2 VJ 
17 29 4.3 

17 45 27.1 

18 1 31.4 
18 17 10.7 
18 32 42.8 

18 47 49.0 

19 2 35.1 
19 17 0.9 

19 31 5.9 

19 41 49.0 

19 58 11.6 

20 11 11.8 
20 23 49.8 

20 30 5.0 

20 47 57.3 

20 5 J 28.2 

21 10 31.5 

21 21 12.9 

21 31 30.0 

21 41 22.7 

S. 21 50 50.5 



Diff. fur 
1 Hour. 



-48.00 
47.42 
46.82 

-46.19 
45.54 
44.89 

-44.21 
43.51 

42.80 

-42.07 
41.32 
40.57 



38.93 
38.10 

-37.34 
3>U9 
35.04 

-34.76 
33.80 
32.90 

-32.03 
31.08 
39.14 

-29.17 

2 3.2 I 
27.21 

-26.21 
25.20 
24.17 

-23.13 



Equation 

of time 

to be 

Subtracted 

from 

Apparent 

Time. 

m. s. 



16 
16 

10 


18.58 
19.48 
19.55 


10 
16 

10 


18.79 
17.19 
14.74 


16 
16 
16 


11.43 

7.27 
2.26 


15 
15 

15 


56.40 
49.08 
42.12 


15 
15 

15 


33.71 
24.47 
14.40 


15 

14 
14 


3.50 

51.78 
39.25 


14 
11 
13 


25.91 
11.77 
50.84 


23 
13 

13 


41.13 
24.63 
7.36 



12 


49.34 


12 


30.5/ 


12 


11.00 


11 


50.83 


11 


29.89 


11 


8.25 


10 4 5.94 



DECEMBER, 1882. 



Apparent 
Declination. 



S.21 50 50.5 

21 59 53.1 

22 8 30.3 

22 16 41.8 

22 24 27.4 

22 31 46.7 



Diff. for 
1 Hour, 



-23.13 
22.07 
21.01 

-19.93 
18.85 
17.75 



22 38 39.7 -16.65 
22 45 6.1 ! 15.53 
22 51 5.5 ! 14.40 



22 56 37.9 

23 1 43.1 
23 6 20.8 

23 10 31.0 
23 14 13.5 
23 17 28.2 

23 20 14.9 
23 22 33.6 
23 24 24.2 

23 25 46.6 
23 26 40.8 
23 27 6.7 

23 27 4.4 
23 26 33.7 
23 25 34.8 

23 24 7.6 
23 22 12.1 
23 19 48.4 

23 16 56.6 

23 13 36.8 

23 9 49.0 

23 5 33.3 

S. 23 49.9 



-13.27 
12.13 

10.98 



8.07 
7.51 

- 6.36 
5.18 
4.01 

- 2.84 
1.67 
0.49 

+ 0.69 
1.87 
3.05 

+ 4.23 
5.40 
6.57 

+ 7.75 

8.91 

10.07 

11.23 

+12.39 



Equation 
ofTime 

to be 

Subtracted ( 

from 



Added lo i 

Apparent , 

Time. 



10 45.94 

10 22.90 

9 59.34 

9 35.11 

9 ,10.29 

8 44.88 

8 18.96 

7 52.55 

7 25.65 

6 58.32 

6 30.59 
6 2.47 

5 34.03 
5 5.30 

4 36.30 

4 7.06 

3 37.64 , 



8.06 , 

38.35 ' 

8.54 ' 

38.68 ' 



1 8.78 
38.89 
9.04 



20.75 

50.44 

1 20.02 



49.45 | 
18.71 
47.77 
16.57 



3 45.11 



13 



SOLAR COMPASS. 



BurPs Solar Compass. 
Was invented in -18.35, by Wiifam A. Burt, U. S. Dep. -Surveyor, and 
and was made under his directiju by William J. Young, of Philadelphia. 
The modern-const ructed'Solar Compass has been adopted by the U.S. 
Government for the Unite 1 States Public Land Surveys. 




The adjustment «.f the ALL Solar Compass is a little complicated, and 
requires a good deal of pa tOP tieiue to do it properly. The most impor- 
tant adjustments are : 

1. That the level bnbbles remain in position by reversing the plates horizontally. 

2. That the equatorial lines and solar lenses are parallel to eac-h other. 

3. That '.he polar axis is at right angle with the axis of the latitude arc. 

4. That the index error of the declination arc is corrected. 
5 That the index error of the latitude arc is adjusted . 

6. That the index error of the hourarc is ascertained 

7. That the lines of the sights are perpendicular 

8. T..at the sights of the compass coincide with the true meridian. 

9. That the compass needle is sensitive 

1 10. That tho variation arc for needle is set to correspond to a true meridian line. 

When all these corrections areft.ccurately made, a final practical trial is effected 
by two morning and afternoon observations If tney give the same result on au 
established true meridian line, then the instrument is in adjustment. 

For more particulars we refer to the " Key of Burt's Solar Compass." 

Meridian Distances West from Greenwich. 



> 101 


6 


44 


111 


> 102 


6 


48 


112 


103 


6 


52 


113 


) 104 


6 


56 


114 


) 105 


7 


00 


115 


) 106 


7 


04 


116 


\ 107 


7 


08 


117 


( 108 


7 


12 


118 


\ 109 


7 


16 


119 


110 


7 


20 


120 



Diff. in 


Time. 


Longitude. 


h 


m. 


o 


7 


24 


121 


7 


28 


122 


7 


32 


123 


7 


36 


124 


7 


40 


125 • 


7 


44 


126 


7 


48 


127 


7 


52 


128 


7 


56 


129 


8 


00 


130 



04 
08 
12 
16 
20 

24 
28 
32 
36 
40 



14 



TAB J, E. 



I FIXED STARS. 

, Mean places of Fifty Principal Fixed Stars, for January 1st, 1882. 



Name of Star. 


Mag 


tlight ascension. 


Anmi 1 

Varu.i li. 


Declination. 


Annual 

Variation. 


( a Andromedce 


2 
2 
3 
2 
2 
2 
2 
3 
2 
2 

3 
3 
3 
1 
1 
1 
2 
2 
2 
2 

1 
2 
2 
1 
3 
2 
1 
2 
3 
2 

2 
1 
2 
1 

2 
2 



2 
1 
2 

3 
2 
3 

1 
2 
1 
2 

a 

2 
1 
2 


li. 






1 
1 
1 
1 

2 

3 
3 
3 
4 
5 
5 
5 
5 
5 
6 

6 

7 
7 
7 
8 
9 

10 

10 

11 
11 

12 
13 
13 

14 
14 

|1« 

15 

15 
16 

it; 

17 
17 
18 
18 
18 
19 
90 
21 
21 
22 
22 


in. 

2 

2 
13 
33 
37 

3 
15 
18 
56 
56 

27 
40 
52 
29 
7 
8 
18 
30 
50 
30 

39 

3 
27 
33 

2 
21 

2 
56 
13 
47 

28 
18 
42 
10 
44 
51 
10 
3« 
22 
25 

3 
29 
20 

32 
47 
45 
37 

25 
88 

51 
58 


17.39 
53.22 
24.80 
49.08 
39.98 

7.08 
30.0} 

7.51 
39.55 

0.70 

22.27 
28.20 
31.48 
9.02 
58.40 
52.03 
4».')8 
13.50 
5?.tl 
5 i.70 

50.91 
35.01 
4.22 
7.47 
31.14 
47.33 
5.22 
20.14 
20.53 
37.20 

11.42 

58.04 
53.44 
16.78 
21.09 
3.70 
39.48 
27.3.; 

io-u 

8.80 

30.05 
27.44 
41.3.) 
50.02 
56.89 
1.57 
24.58 
2 ».8 ) 
23.45 


B. 

+ 3.090 
" 3.170 
" 3.053 
" 3.370 
" 3.015 
" 3.342 
" 21.905 
2.997 
" 3.653 
" 3.1 ;;) 

" 2.823 

3.3 30 

2.798 

" 3.430 

4.424 

" 2.831 

3.789 

" 3.342 

" 4-413 

" 3,468 

" 2.644 
" 2.438 

3.8*9 
" 3.141 
" 2.554 
" 2.949 
» 3.231 
» 3.754 
» 2.990 

c.185 

« 3.140 
3.153 

" 2.372 

" 2.735 

" 3.308 

- 0.2 9 

+ 3.221 

2.951 

3.669 

2.57 7 

•■ 3.436 
2.783 

• 4 3.703 

" 2.031 
3.722 

•' 2.928 
2.044 
3.102 

" 2.917 
3.326 


O / / / 

+ 28 26 20.0 
" 58 29 55.0 

- 9 28 42.2 
+ 55 53 23.7 

18 38 4.0 
+ -A 59 40.4 
" 88 40 40.9 

- 8 47 33.5 
+41 45 45.7 
" 3 37 3". J 

- 9 51 30.2 
+ 23 44 23.5 

- 13 50 42.0 
+ 16 16 14.8 
"45 52 34.3 

- 8 20 20.8 
+ 28 30 22.4 

- 1 16 42.6 
+ 44 56 0.15 

• 16 29 55.0 

-16 33 19.1 

• 26 12 24.1 
+32 8 45.4 
" 5 31 34.0 

23 57 53.8 
"88 52.3 
+ 12 32 30.1 
" 02 23 15.9 
-14 8 24.9 
+ 54 21 2.7 

-22 44 38.5 
" 10 32 42.1 
+ 49 54 9.1 
11 19 47 50.2 
15 33 2.1 
+ 74 38 15.8 

- 8 56 47.8 
+ 6 47 51.7 
-20 10 7.7 

21 44 51.0 

-15 34 39.1 
+12 38 49.0 

25 29 7.7 
+ 38 40 28.1 

20 20 30.0 

+ 8 33 27.4 

" 44 51 32.9 

5 22.0 

+ 9 20 4-5 

30 14 50.2 

11 34 14.0 


// 

+ 19.89 
" 19. 5 


) t Ceti 


" 19.96 


)a C.issipete (var.) .. 
) {} Ceti 


« 19.79 
" 19+1 


> /3 Amiromedaj 

)a CJrs. Mln.( Polaris). 
r a' Ueti 


" 19.18 
" 18.98 
" 18.18 


(y Andromedce 

( a. Ceti 


" 17.46 
'• 14.3J 


( € Eridani 


" 12-42 




11 11.41 




" 10.47 


)a Tauri (Aldebaran). 
)a Auriga (Capella).. 
)j3 Orients (Rigel) .... 
) j3 Tauri 


" 7.55 
" 4.08 
" 4.43 
" 3.40 




" 2.00 


S/3 Aurigse 

Sy Ge minor urn 

Sa CanisMaj.(Sirius.. 

)8 Canis MajorU 

( a2 Geminor'm(Castor 
{aCanisMin.(Procyon 

(15 Argus(J) 

(a Hydraa 


" 0.79 
- 2.74 

" 4.68 
" 5.48 
" 7.52 
11 8.96 
" 10.17 
" 15.43 


a Leonis(Regulus .. 

?a Ursie Majoris 

(5 Crateris 


11 17.46 

" 19.' , 5 
" 19.46 


) y U raw Maj oris 

)/3 ttorvi 


11 20.03 

" 19.97 


)a \ irginia (Spica 

Stj Urs. Maj. (Alioth . 

(a Bootis (Arcturus.. 
( a2 Libne 


" 18.91 
" 18.09 
" 18.90 
" 15.19 


( /3 Urs.B Minoris 

( j3 Libra 


" 14.72 
11 13.54 


f a S.-rpMitis 

) a Scnrpii (Antarea .. 
) fi Herculii 


" 8-34 
" 8-08 


Srj Ophiuchl 


M 4.78 


S a Qphiucki 


" 2.90 


\ A Sagittarii 


+ 1.00 


(a Lyra (Vega 

(a Sagittarii 


" 3.15 

" 4.09 


fa Aipiilae (Altair . . . 

/a Cygnl 

)fi Aquarii 

B isii 


11 9.24 
" 12.71 
44 15.64 
M 10/4 


i h-.AiH. ( Komalh'l 
« P gasi(M .rka'»... 


" 1&98 

" 19.29 



15 



TABLE 

Of Refractions in Declination for Solar-Compasses and Solar-Transits. 



T 



Plus: 

April. 

May. 
i June. 
! July 

I August. 







Br Sun 


's Declination 


3 Forth, 


V 


From March 22d to Sept. 22d, add: 






\ 


For 


Hours 
from 


Sun's Declinations in Nautical Aim. 


\ 


Lati. 


Me id. 


+ 23° 


4- 15^ 


+ loo 


+ 50 ( 


\ 




/ // 


/ // 


/ // 


/ // ( 


\ 


30° 


1. 


10 


15 


21 


27 ( 


\ 


'« 




14 


19 


25 


31 < 


\ 


44 




20 


26 


32 


39 < 


\ 


.( 




32 


39 


46 


52 


\ 


35° 




15 


21 


27 


33 ( 


\ 


»« 




20 


25 


32 


38 < 


1 


« 




26 


33 


39 


47 


1 


♦i 




39 


47 


56 


1 06 


J 


40° 




21 


27 


33 


40 


I 


" 




25 


32 


39 


46 


I 


u 




33 


40 


48 


57 


1 


ii 




47 


55 


1 05 


1 18 


J 


45° 




27 


33 


40 


48 


1 


" 




32 


39 


46 


52 


J 


ii 




40 


47 


56 


1 06 


1 


u 




54 


1 02 


1 14 


1 32 { 


/ 


50° 




33 


40 


48 


57 


/ 






38 


46 


55 


1 06 


/ 


44 




47 


56 


1 06 


1 20 


/ 


" 




1 00 


1 45 


2 00 


3 00 


Minus: 

Oct 




By Sui 


i's Declinations South, < 


Fro 


in Sept. 


22d to March 22d, substraci : ( 




For 


Hours 

from 


Sun's Declinations in Nautical Aim. 








Nov. 


Lati. 


Merid. 


- 50 


- 10O 


- 150 


- 20O J 






/ // 


/ // 


' "~ 


A ,, < 




30° 


1. 


40 


48 


56 


1 00 




» 


2. 


46 


54 


1 10 


1 18 




ii 


3. 


55 


1 06 


1 18 


1 36 ( 


Dec. 


ii 


4. 


1 19 


1 35 


1 57 


2 29 < 


35° 


1. 


48 


57 


1 06 


1 20 J 




" 


2. 


55 


1 04 


1 18 


1 34 




44 


p # 


1 06 


1 20 


1 40 


2 00 < 


Jan. 


44 


4. 


1 40 


2 00 


2 30 


3 30 < 


40° 


1. 


1 00 


1 08 


1 30 


1 40 J 




44 


2. 


1 08 


1 20 


1 36 


2 00 


— 


44 


3. 


1 20 


1 40 


2 00 


2 40 < 




•t 


4" 


2 00 


2 30 


3 20 


5 00 ( 


Feb. 


45° 


I. 


1 08 


1 30 


1 40 


2 00 { 




• 4 


2. 


1 20 


1 40 


2 00 


2 CO S 


— 


•" 


3. 


1 40 


2 00 


2 36 


3 30 < 




44 


4. 


2 20 


3 00 


4 40 


8 00 ( 


March. 


50° 


1. 


1 30 


1 40 


2 00 


2 40 S 




'• 


2. 


1 36 


2 00 


2 30 


3 15 \ 


: -22d- 


•' 


:'. 


2 30 


2 45 


3 30 


5 00 S 


" 


i. 


3 00 


4 30 


7 00 


15 00 S 







16 



T A 13 L E . 

Of the Increase or decrease of the Sun's Declination for hourly Differences, 
from 5 seconds to GO seconds, ami from three to twelve hours of time. 



dif. 


3 1 . 


// 


/ 


// 


5 




15 


(5 




18 


7 




21 


8 




24 







27 


10 




30 


11 




33 


12 




30 


18 




39 


14 




42 


16 




45 


10 




48 


17 




51 


18 




54 


19 




57 


20 


1 


00 


21 


1 


03 


22 


1 


06 


23 


1 


09 


24 


1 


12 


2.1 


1 


15 


26 


1 


18 


27 


1 


21 


28 


1 


24 


20 


1 


27 


3.) 


1 


30 


31 


1 


33 


33 


1 


36 


S3 


1 


39 


31 


1 


42 


S 5 


1 


45 


3; 


1 


48 


37 


1 


51 


33 


1 


54 


3.) 


1 


57 


40 


2 


00 


41 


2 


03 


42 


2 


00 


43 


2 


09 


44 


2 


12 


4T, 


2 


15 


40 


2 


18 


47 


2 


21 


48 


2 


24 


4'.» 


2 


27 


60 


2 


30 


51 


2 


33 


62 


2 


30 


68 


2 


39 


64 


2 


42 


55 


2 


45 


56 


2 


48 


57 


2 


51 




2 


54 


59 


a 


57 




3 


00 



1 36 

1 40 

1 44 

1 48 

1 52 

1 56 

2 00 



2 
2 
2 
2 

2 
2 
2 
2 
2 
2 

2 
2 
2 
2 
3 
3 
3 
3 
3 
3 

3 

3 

3 

3 

3 

3 44 

3 48 

3 52 

3 56 

4 in) 





' , 


/ 


// 




25 




30 




85 




40 




45 




50 




55 


1 


00 


1 


05 


1 


10 


1 


15 


1 


20 


1 


25 


1 


30 


1 


35 


1 


40 


1 


45 


1 


50 


1 


55 


2 


00 


2 


05 


2 


10 


2 


15 


2 


20 


2 


25 


2 


30 


2 


35 


2 


40 


2 


45 


2 


50 


2 


55 


3 


00 


3 


05 


3 


10 


3 


15 


3 


20 


3 


25 


3 


30 


3 


35 


3 


4(1 


3 


45 


3 


50 


3 


55 


4 


00 


4 


05 


4 


10 


4 


15 


4 


20 


4 


25 


4 


30 


4 


35 


4 


in 


4 


45 


4 


50 


4 


55 


5 


01 



6 h. 


7 h. 


/ 


// 


/ 


// 




30 




35 




30 




42 




42 




49 




48 




50 




54 


1 


03 


1 


00 


1 


10 


1 


00 


1 


17 


1 


12 


1 


24 


1 


18 


1 


31 


1 


24 


1 


38 


1 


30 


1 


45 


1 


3,0 


1 


52 


1 


42 


1 


59 


1 


4S 


2 


00 


1 


54 


2 


13 


2 


00 


2 


20 


2 


00 


2 


27 


2 


12 


2 


34 


2 


18 


2 


41 


2 


24 


2 


48 


2 


30 


2 


55 


2 


30 


3 


02 


2 


42 


3 


09 


2 


48 


3 


16 


2 


54 


3 


23 


3 


00 


3 


30 


3 


00 


3 


37 


3 


12 


3 


44 


3 


18 


3 


51 


3 


24 


3 


58 


3 


30 


4 


05 


3 


30 


4 


12 


3 


42 


4 


19 


3 


48 


4 


20 


3 


54 


4 


33 


4 


03 


4 


40 


4 


00 


4 


47 


4 


12 


4 


54 


4 


18 


5 


01 


4 


24 


5 


08 


4 


30 


5 


15 


4 


30 


5 


22 


4 


42 


5 


29 


4 


48 


5 


30 


4 


54 


5 


43 


5 


00 


5 


50 


5 


0<J 


5 


57 


5 


12 





01 


5 


13 





11 


5 


2j 





18 


5 


30 





25 


5 


26 





32 


5 


42 





39 


5 


48 





40 


5 


54 





53 





00 


7 


00 



8 },. 


/ 


// 




40 




48 




56 


1 


04 


1 


12 


1 


20 


1 


28 


1 


30 


1 


44 


1 


52 


2 


00 


2 


08 


2 


10 


2 


24 


2 


32 


2 


40 


2 


48 


2 


50 


3 


04 


3 


12 


3 


20 


3 


28 


3 


30 


3 


44 


3 


52 


4 


00 


4 


08 


4 


10 


4 


24 


4 


32 


4 


40 


4 


48 


4 


50 


5 


04 


5 


12 


5 


20 


5 


28 


5 


30 


5 


44 


5 


52 


6 


00 





08 





10 





21 





32 





40 





48 


o 


50 


7 


04 


7 


12 


7 


20 


7 


28 


7 


30 


7 


44 


7 


52 


B 


00 



9 k 10 h. 11 h. 12 1, 



7 39 

7 48 

7 57 

8 0G 
8 15 
8 24 
8 33 
8 4 2 
8 51 

g oo 



10 
6 20 



50 



3 40 



6 58 

7 09 
7 20 



7 31 

7 42 

7 53 

8 04 
8 15 
8 20 
8 37 
8 48 

8 59 

9 10 



10 00 



10 


12 


10 


24 


10 


36 


1(1 


18 


11 


00 


11 


12 


11 


•Jl 


11 


30 


11 


48 


u 


00 



17 



SOLA R T R A N S I T. 



INVENTED by WM. SCHMOLZ. 
Patent No. 72687. Dated December 24th, 1S67. 




Present owners of the Patent, W & L. E. GURLEY, Troy, N. Y. 



18 



DESCRIPTION OF THE SOLAR TRANSIT. 



(Fkom thk "Alt a California," Jan. 4'h, 18G8.) 

"For many years Win. Schmolz devoted hid leisure hours to the special 
study of thc'Solar Compass, and the m >re he became acquainted with the prin- 
ciples of the instrument, t lie higher he appreciated the Invention of W, S. I>urt. 

" The advantages which the solar apparatus possesses over all other instru- 
ments constructed for the U.S. Public Land Surveys arc undisputed , it La 
plcte Instrument ; and still the e is a defect, existing In the compass sights, 
vchlch makes the instrument unreliable in mountainous regions to establish aline 
correctly. Many attempts which have been made to attach a telescope to a So- 
lar Compass never amounted to a decided success. Seeing the Impossibility of 
attaching a telescope to a 'Solar,' Mr. Schmolz male some experiments in 
plating a declination arc on a Transit, and found that the trial observations gave 
a satisfactory result ; and b sing c mvinced of the originality of his construction, 
he applied for a United States patent, which was granted to him last week. 

" We suppose that the reader is alrealy familiar with the principles of the 
Solar Compass, as well as with the construction of the Transit ; so that In this 
case it is easy for us to describe the invention, as th ! only piece around which 
the invention turns is merely a small spindle attached to the top in the middle, 
aid perpendicular to the telescope ax's and the optical axis of an ordinary 
Transit. This center spindle is exiled the 'Polar Axis, ' to which an hour arc 
and a declination arc, &c., are attached. 

" For new beginners it w 11 be an interesting study to get acquainted with 
the Ave movements which a Solar Transit has: I. The Declination ; 11. Tlie 
Equatorial; III. The Vertical; IV. The Horizontal; V. The Meridian. 
If those movements are well understood, then the principal at cntion has to be 
directed to the increase or decrease of Declination, Meridian Distance, and Re- 
fraction. 

"The adjustment of Schmolz's Solar Transit is a combination of two distinct 
Instruments: I. T:ie Transit. 

" 1. That the levels remain in posiiion by repeatedly reversing. 

"2. That the gross hairs are in perfect collimation. 

" 3. That the telescope describes a perpendicular hue. 

■* 4. That the telescope level is parallel to the optical axis. 

" 5. That the verni.r of the elevation arc is at zero. 

"6. That the compa;s needle is sensitive, and is well adjnsted, 

lk 7. That the index error of the coaipas3 needle U ascertained on a true me- 
ridian. 

"II. The Solar Apparatus Adjustment is precisely the same as that of the 
Solar Compa*. 

M With several friends we have seen the progress of the instrument, and were 
very much pleased when the portable astronomical observatory was finished, 
We witnessed yesterday the expert m -at il observations, and were astonished at 
the precision with which meridian lines, variation of the compass needle, time 
of the day, latitude and longitude, were repeatedly established." 

San Francisco, Jan. 4th, 1SS2. 
Several Solar Transits have been cons-tructed and patented since the above 
patent was issued ; but none has given such entire satisfaction, or is manufac- 
tured so extensively, or is so generally in practical Use, W the I DC d< > I 
jealousy of some Philadelphia makers lias led them to disparage the instrument ; 

but in a few years, , wh in the term of the patent will have expired, they will be 
-i to adopt Schmolz's const ru ii in. 



W. s. 



T A 111, K. 



AZIMUTHS OF POLARIS, 

At the time of greatest elongation, from the year 1881 to 1900, 
and from latitude 30deg. to 49deg. north. 



Computed by W. J. Lewis, C. E. 
For W. Scbmolz, San Francisco, Cal. 



year. 


L. 

o 


30° 


L.31° 


L. 323 


L. 

o 


35° 


L. 


340 


L. 


35° 


L. 


36- 

/ 


L.37° 


L. 

D 


38° 

/ 


|] . 

"0 


39° 


yeur.( 




/ 


o 


/ 


o 


/ 


~ 7\ o 


/ 


°~ 


/ 


— 






/ 


/ 




1881. 


1 


32 


1 


33 


1 


34 


1 


35! 1 


36 


1 


37 


1 


38 


1 


40 


1 


41 


' 1 


42 


1881-C 


1882. 1 


31 


1 


32 


1 


33 


1 


34! 1 


36 


1 


37 


1 


38 


1 


39 


1 


41 


1 


42 


1882-C 


188?. 


1 


31 


1 


32 


1 


33 


1 


34! 1 


35 


1 


36 


1 


38 


1 


39 


1 


40' 1 


42 


188£< 


1881. 


1 


31 


1 


32 


1 


33 


1 


34 ; 1 


35 


1 


36 


1 


37 


1 


38 


1 


40 1 


41 


1884./ 


1885. 


1 


30 


1 


31 


1 


32 


1 


33 1 


34 


1 


36 


1 


37 


1 


38 


1 


39 


1 


41 


1885.) 


188C. 


1 


30 


1 


31 


1 


32 


1 


33 1 


34 


1 


35 


1 


36 


1 


38 


1 


39 


1 


40 


1886.) 


1887. 


1 


30 


1 


31 


1 


32 


1 


33! 1 


34 


1 


35 


1 


36 


1 


37 


1 


39. 1 


40 


1887.) 


1888. 


1 


29 


1 


30 


1 


31 


1 


32! 1 


33 


1 


34 


1 


36 


1 


37 


1 


38 1 


39 


1888.) 


1889. 


1 


29 


1 


30 


1 


31 


1 


32! 1 


33 


1 


34 


1 


35 


1 


36 


1 


38 1 


39 


188P.) 


1800. 


1 


29 


1 


29 


1 


30 


1 


81 j 1 


32 


1 


34 


1 


35 


1 


36 


1 


37 


1 


39 


1890.) 


1891. 


j ! 


28 


1 


29 


1 


30 


1 


31: 1 


32 


1 


33 


1 


34 


1 


36 


1 


37 


1 


38 


1891.S 


18132. 


1 


28 


1 


29 


1 


30 


1 


31: 1 


32 


1 


33 


1 


34 


1 


35 


1 


37 


1 


38 


1892A 


1893. 


1 


27 


1 


28 


1 


29 


1 


30i 1 


31 


1 


32 


1 


34 


1 


35 


1 


36 


1 


37 


1893.C 


1891. 


1 


27 


1 


28 


1 


29 


1 


30 ; 1 


31 


1 


32 


1 


33 


1 


34 


1 


36 


1 


37 


1894.C 
1895.' 


1895. 


1 


27 


1 


28 


1 


29 


1 


30! 1 


31 


1 


32 


1 


33 


1 


34 


1 


35 


1 


37 


1896. 


1 


26 


1 


27 


1 


28 


1 


29! 1 


30 


1 


31 


1 


32 


1 


34 


1 


35 


1 


36 


1896/ 


1897. 


1 


26 


1 


27 


1 


28 


1 


29! 1 


30 


1 


31 


1 


32 


1 


33 


1 


35 


1 


36 


1897.) 


1898. 


1 


26! 1 


27 


1 


27 


1 


29! 1 


29 


1 


31 


1 


32 


1 


33 


1 


34 


1 


35 


1898/ 


1899. 


1 


25 


1 


26 


1 


27 


1 


28! 1 


29 


1 


30 


1 


31 


1 


32 


1 


34 


1 


35 


189?. J 


1900. 


1 


25 


1 


26 


1 


27 


1 

L. 

Q 


28 

433 


1 


: 9 


1 

I. 



30 

45° 
/ 


1 


31 


1 


32 


1 


33 


1 


34 


1900/ 

— 1 




L. 


40° 


Q 


11° 

/ 


L. 

o 


42° 

/ 


L. 


44- 


L. 



460 


L. 470 


1, 


48^ 


L. 49° 


\ 







/ 


Q 


~7 


Q 


/ 


Q 


/ 


Q 


/ 


) 


1881. 


1 


44 


1 


45 


1 


47 


1 


49! 1 


51 


1 


52 


1 


54 


1 


57 


1 


59 


2 


01 


1881/ 


1832. 


1 


43 


1 


45 


1 


47 


1 


48! 1 


50 


1 


52 


1 


54 


1 


56 


1 


58 


2 


01 


1882.) 


1883. 


1 


43 


1 


45 


1 


46 


1 


48! 1 


50 1 1 


52 


1 


54 


1 


56 


1 


58 


2 


00 


188J.) 


1884. 


1 


ii 


1 


44 


1 


46 


1 


47 


1 


49 


1 


51 


1 


53 


1 


55 


1 


57 


2 


00 


1884.) 
1885. 1 ) 


1885. 


1 


42 


1 


44 


1 


45 


1 


47 


1 


49 


1 


51 


1 


53 


1 


55 


1 


57 


1 


59 


1886. 


1 


42 


1 


43 


1 


45 


1 


47 


1 


48 


1 


50 


1 


52 


1 


54 


1 


56 


1 


59 


1886.S 


1837. 


1 


41 


1 


43 


1 


44 


1 


46 


1 


48 


1 


50 


1 


52 


1 


54 


1 


56 


1 


58 1887A 


1888. 


1 


41 


1 


42 


1 


44 


1 


46 


1 


47 


1 


49 


1 


51 


1 


53 


1 


56 1 


58 1888.S 


1889. 


1 


41 


1 


42 


1 


44 


I 


45 


1 


47 


1 


49 


1 


51 


1 


53 


1 


55 1 


57 


1889.C 


1890. 


1 


40 


1 


42 


1 


43 


1 


45 


1 


47 


1 


48 


1 


50 


1 


52 


1 


55 


1 


57 


1890/ 


1891. 


1 


40 


1 


41 


1 


43 


1 


44 


1 


46 


1 


48 


1 


50 1 


52 


1 


54 


1 


56 


1891/ 


1892. 


1 


39 


1 


41 


1 


42 


1 


44 


1 


46 


1 


48 


1 


50 


1 


52 


1 


54 


1 


56 


1892.) 


1893. 


1 


39 


1 


40 


1 


42 


1 


44 


1 


45 


1 


47 


1 


49 


1 


51 


1 


53 


1 


55 


1893.) 


1894. 


1 


38 


1 


40 


1 


41 


1 


43 


1 


45 


1 


47 


1 


49 


1 


51 


1 


53 


1 


55 


1894.) 


1895. 


1 


38 


1 


40 


1 


41 


1 


43 


1 


44 


1 


46 


1 


48 


1 


50 


1 


52 


1 


54 


1895.S 


1896. 


1 


38 


1 


39 


1 


41 


1 


42 


1 


44 


1 


46 


1 


48 


1 


50 


1 


52 


1 


54 


1896 ( 


1897. 


1 


37 


1 


39 


1 


40 


1 


42 


1 


44 


1 


45 


1 


47 


1 


49 


1 


51 


1 


54 


1897A 


1898. 


1 


37 


1 


38 


1 


40 


1 


41 


1 


43 


1 


45 


1 


47 


1 


49 


1 


51 


1 


53 


1898.C 


1899. 


1 


3G 


1 


38 


1 


39 


1 


41 


1 


43 


1 


44 


1 


46 


1 


48 


1 


50 


1 


53 


1899.< 


1900. 


1 


30 


1 


37 


1 


39 


1 


41 


1 


42 


1 


44 


1 


46 


1 


48 


1 


50 


1 


52 


19007 



20 



TABLES. 



1 The following Tables give the greatest Eastern and Western Elongation of the North' i 
Star (Polaris), in common clock time, for every third day in the^'ear when the star ( 
is visible, •* 



EASTERN ELONGATION. 


Day 

of 
M onth 


April. 


May. 


June. 


July, 
li. min. 


I August. 
i h. min. 


September, 
h. min. 




h. min. 


h. min. 


h. min. 


1 


6 39 A.M 


4 41 A.M 


2 39 A.M 


41 A.M 


: 10 35 P.M 


8 32 P.M 


4 


6 27 " 


4 29 " 


2 28 " 


30 m 


i 10 23 " 


8 20 " 


7 


C 15 M 


4 17 M 


2 16 " 


18 «« 


10 12 M 


8 08 " 


10 


6 03 " 


4 05 " 


2 04 " 


06 « 


10 00 " 


7 56 " . 


13 , 


5 52 ,4 


3 53 " 


1 52 " 


11 49 T.M 


9 48 " 


7 45 " • 


10 


5 40 " 


3 41 " 


1 40 " 


11 37 " 


9 36 " 


7 33 M ) 


19 


J> 28 •< 


3 30 " 


1 28 " 


11 25 " 


9 24 " 


7 21 " . 


22 


5 16 " 


3 18 M 


1 17 " 


11 14 " 


9 12 " 


7 09 " 


25 


5 04 M 


3 06 " 


1 05 " 


11 02 " 


9 01 " 


6 57 " 


28 


4 52 M 


2 54 " 


53 " 


10 50 " 


8 49 " 


6 46 " 


31 





2 42 " 





10 38 " 


8 37 m 


{ 






WESTERN ELONGATION 




. i 


Day 

of 
Month 


October. 


November. 


December. 


January. 


February. 


March. 




h. min. 


h. min. 


h. min. 


h. min. 


h- min. 


h. min. 


1 


6 27 A.M 


4 24A.M 


2 26 A.M 


27 A.M 


10 21 P.M 


8 31 ,P S M 


4 


6 15 M 


4 13 " 


2 14 " 


15 m 


10 09 " 


8 18.." 


7 


6 03 M 


4 01 " 


2 02 " 


12 00 P.M 


9 58 ° 


8 OG " 


10 


5 61 m 


3 49 " 


1 51 " 


11 48 " 


9 46 " 


7 55 ■ 


13 


5 39 M 


3 37 ■« 


1 39 " 


11 36 " 


9 34 " 


7 44 « 


1G 


5 27 " 


3 25 "■ 


1 27 " 


11 24 " 


9 22 M 


7*32 " 


19 


5 16 M 


3 13 «« 


1 16 " 


11 12 " 


9 10 " 


7 20 tf 


22 


5 04 " 


3 02 ■« 


1 04 " 


11 01 " 


8 59 " 


7 08 f< 


25 


4 52 M 


2 50 ■« 


52 M 


10 49 " 


8 47 " 


6 56 ° 


28 


4 40 " 


2 38 " 


41 " 


10 36 " 


8 35 " 


6 44 " 


31 


4 28 " 


30 " 10 25 »« 


! 


6 33 V 



An approximation to the true meridian might be ob- 
| tained by sighting on the Pole Star at the instant when 
It is on tne same vertical plane with Alioth. The North 
1 Star is exactly in the true meridian 26 minutes in time 
i after it has been in the same vertical plane with Alioth, 
i and may be sighted after that interval of time with per* 
i feet accuracy. 

On the first day of January, 1SS2, the right ascen- 

slonof Polaris will be: lh. 15 in. 30 sec., and of Alioth 

13 h. 43m. C3 see. "When therefore Polaris arrives at 

1 the meridian, Alioth will be 27 m. 23 sec. to the East. 

Hence when Alioth is directly under Polaris, or in 

I the same vertical plane, the pole is to the West of thii 

i plumb line, ranging from lOmin. 33 sec. in arc in lat. 

, 30deg. north to 14 min. 2sec. inlat. 4!) deg. north. 

. The azimuth for every second degree of latitude Is 
. shown in the following table: 



eh 



Lat. 


m. b. 


Lat. 


m. s. 


Lat. 


m. s. 


900 


10 '21 


36^ 


11 23 


443 


19 48 


30^ 


10 38 


38^ 


11 41 


460 


13 15 


82° 


10 51 


40° 


19 01 


483 


13 4G 


340 


11 06 


UP 


12 23 


49° 


14 02 



21 



EXPLANATORY NOTES. 



EXPLANATION OF THE TABLES, 



Tables I and II. 

Table I gives the length of a degree Qf latitude, in chains, for every minute of 
latitude between 29 and 49 degrees, calculated by the Formula Dm — 5523. S724— 
27.7425 coa 2 I -\- .0592 cos 4 Z, in which Dm represents a degree of the meridian, 
and I, the middle latitude. 

Table II gives the length of a degree of longitude, in chains, for every minute of 
latitude between 29 and 49 degrees, calculated by the formula Dp = 5o37.7439 cos I 
—4.6337 cos 3 I + .0058 cos 5 J, in which Dp represents a degree of the parallel and 
I, the latitude. 

These tables are useful for converting linear into angular, and angular into linear 
measure, as well as for determining the convergences and divergencies of the 
meridians, on the spheroidal surface of the earth. 

PROBLEMS AND EXAMPLES. 

1. Given the latitudes of any two places on the same meridian, to 

find the distance between them. 
"Rule.— Find, from Table I, the length of a degree of the meridian at each 
latitude, and take half their sum for the mean length of a degree. Then say, as 60 
minutes is to the difference of latitude, so is the mean length of a degree to the 
distance required. 

The latitude of the Monte Diablo Base Line, is 37 deg. 52 min. 47 sec., and that 
of the 1st Standard North, 38 deg. 18 min. 53 sec. ; what is the meridional distance 
between them? 

chains. chains. 
As 60 min. : 26 min. 6 sec. : : 5517.205 : 24,00 the distance required. 

2. Given the distance between any two places on the same meridian, 
and the latitude of one of them to find their difference of latitude. 

Rule.— Find, from Table I, the length of a degree of the meridian, in the 
given latitude, and also in that differing from it, by the meridional distance, 
converted into ah arc at the rate of 52 seconds per mile, and take half their sum 
for the mean length ot a degree. Then say, as the mean length of a degree 
is to the meridional distance, so is 60 minutes to the difference of latitude re- 
quired. 

The latitude of the Monte Diablo Base Lino, is 37 deg. 52 min. 47 sec; what is 
the latitde of the 1st Standard North, the meridional distance being 30 miles ? 
chains. chains. 
As 5517.205 : 2400 : : 60 min. : 26 min. 6 sec, the difference of latitude required. 

3. Given the longitudes of any two places, on the same parallel, in a 

given latitude, to find the distance between them. 

Rule.— Find, from Table II, the length of a degree of longitude in the given 
latitude : and say, as 60 minutes is to the difference of longitude, so is the 
length of the degree of longitude to the distance required. 

The longitude of Monte Diablo Meridian is 121 deg. 54 min. 49 sec., and that 
of Range 1 East, 121 deg. 21 min. 53 sec; what is the distance between them, on 
the Base Line, in latitude 37 deg. 52 min. 47 sec? 

chains chains 
As 60 min. : 32 min. 56 sec. : : 4372.51 : 2400, the distance required. 



22 



E X P L A NATO R V X O T K S. 



4. Given the distance between any two places on the same parallel, 

in a given latitude^ to find their difference of longitude. 

Rule.— Find from Table II, the length of degree of longitude in the given 
latitude ; and say, as the length of the degree of longitude is to the given distance, 
so is CO minutes to the difference of longitude. 

The longitude of the Monte Diablo Meridian, is 121 deg. 51 inin. 40 sec.: what is 
the difference of longitude to Range S East, the distance on the Base Line, in 

latitude 37 deg. 52 inin. 47 sec., being 30 miles? 
chains, chains. 
As 4373.51: 2400: • 60 min.: 32 min. 50 sec, the difference of longitude required. 

5. Given the distance between two meridians, on any parallel, in a 

given latitude, to find the couvergcncy of the meridians for any 

distance north of that parallel. 
Rule.— Find the length of a degree of longitude, at each latitude, by the fore- 
going rules ; and say, as the greater of the two lengths is to their difference, so is 
the given distance to the convergency required. 

The distance between Ranges 1 and 2 on the 1st Standard South, is G miles, 
what is the convergency of the two range lines at the 2d Standard North, the me. 
rldiouai distance being 30 miles? 

chains, chains, chains, chains. 
As 4346. CO : 26.07 : : 480 : 2.83, the convergency required. 

6. Given the distance between two meridians, on any parallel in a 
given latitude, to find the divergency of the meridians for any 
distance south of that parallel. 

Rule,— Find the length of a degree of longitude, at each latitude, by the tore- 
going rules ; and say, as the less of the two lengths is to their difference, so is 
the given distance to the divergency required. 

The distance between Ranges 1 and 2, on the 1st Standard South, is 6 miles ; 
what is the divergency of the two range lines at the 2d Standard South the 
meridional distance being 24 miles? 

chains, chains, chains, chains. 
As 4393.00 : 20.34 : : 4S0 : 2.22, the divergency required. 

Table III. 

> 

This table gives the divergency of the Parallel of Latitude from the Prime ) 

Vertical,* or perpendicular to the meridian, on the spheroidal surface of the earth' ) 

at every second degree of latitude, from 23 to 43 degrees, for any number of ) 

miles from 1 to 36; and is useful in running a parallel of latitude by fore and ) 

back sighting. ) 

•The length of a degree of the Prime Vertical may be calculated by the Formula \ 
Dv = 5551. •".: is — i -.0536 coa H +.0940 cos 4 l ; in whieii Dv represents a degree of 

the Prime Vertical, in chains, and I the latitude. r 

E X A M P L E. ) 

If a line commenced on the parallel of 37 degrees north latitude, be extended - 
east or west, 27| miles, by fore and back sighting, what distance will its terminus ) 
be south of that parallel? \ 

chains. 
The table gives for 27 miles in latitude 37 deg. 6 69 

594 

The mean of which it 6,78 the distance required. 

29 



TABLE. I- 
Length of a Degree of Latitude. 



chains. 

5509-15 
09-16 
09-17 
09-19 
09-20 
09-21 
09-23 
09-24 
09-25 
09-27 
09-28 
09-30 
09-31 
09-32 
09-34 
09-35 
09-36 



09-41 
09-42 
09-43 
00-45 
09-46 
09-47 
09-49 
09-50 
09-51 
09-53 
09-54 
09-56 
09-57 
) 32j 09-58 
09-60 
09-61 
09-63 
03-64 
09-65 
09-67 
09-68 
09-69 
09-71 
09-72 
09-74 
09-75 
09-76 
09-78 
09-79 
09-80 
09-82 
09-83 
09-85 
09-86 
09-87 
09-89 
09-90 
09-92 
09-93 
09-94 
09-96 
09-97 



30° 


310 


32° 


33° 


340 


chains. 


chains. 


chains. 


chains. 


chains. 


5509-97 


5510-82 


5511-67 


5512-55 


5513-44 


09-99 


10-83 


11-69 


12-56 


i 13-45 


10-00 


10-84 


11-70 


12-58 


13-47 


10-01 


10-86 


11-72 


12-59 


13-48 


10-03 


10-87 


11-78 


12-61 


13-50 


10-04 


10-89 


11-75 


12-62 


13-51 


10-06 


10-90 


11-76 


12-64 


13-53 


10-07 


10-91 


11-78 


12-65 


13-54 


10-08 


10-93 


11-79 


12-67 


13-56 


10-10 


10-94 


11-81 


12-68 


13-57 


10-11 


10-96 


11-82 


12-70 


13-59 


10-13 


10-97 


11-83 


12-71 


13-60 


10-14 


10-99 


11-85 


12-73 


13-62 


10-15 


11-00 


11-86 


12-74 


13-63 


10-17 


11-01 


11-38 


12-76 


13-65 


10-18 


11-03 


11-89 


12-77 


13-66 


10-19 


11-04 


11-91 


12-79 


13-68 


10-21 


11-06 


11-92 


12-80 


13-69 


10-22 


11-07 


11-94 


12-81 


13-71 


10-24 


11-09 


11-95 


12-83 


13-72 


10-25 


11-10 


11-96 


12-84 


13-74 


10-26 


11-11 


11-98 


12-86 


13-75 


10-28 


11-13 


11-99 


12-87 


13-77 


10-29 


11-14 


12-01 


12-89 


13-78 


10-31 


11-16 


12-02 


12-90 


13-80 


10-32 


11-17 


12-04 


12-92 


13-81 


10-33 


11-19 


12-05 


12-93 


13-83 


10-35 


11-20 


12-07 


12*95 


13-84 


10-36 


11-21 


12-08 


12-96 


13-86 


10-38 


11-23 


12-10 


12-98 


13-87 


10-39 


11-24 


12-11 


12-99 


13-89 


10-41 


11-26 


12-12 


13-01 


13-90 


10-42 


11-27 


12-14 


13-02 


13-92 


10-44 


11-29 


12-15 


13-04 


13-93 


10-45 


11-30 


1217 


13-05 


13-95 


10*46 


11-31 


1218 


13-07 


13-96 


10-48 


11-33 


12-20 


13-08 


13-98 


10-49 


11-34 


12-21 


13-10 


13-99 


10-50 


11-36 


12-22 


1311 


14-01 


10-52 


11-37 


12-24 


1313 


14-02 


10-53 


11-39 


12-26 


13-14 


14-04 


10-55 


11-40 


12-27 


13-16 


14-05 


10-56 


11-42 


12-29 


13-17 


1407 


10-57 


11-43 


12-30 


13-18 


14-08 


10-59 


11-44 


12-31 


13-20 


1410 


10-60 


11-46 


12-33 


13-21 


1411 


10-62 


11-47 


12-34 


13-23 


14-13 


10-63 


11-49 


12-36 


13-24 


14-14 


10-65 


11-50 


12-37 


13-26 


14-16 


10-66 


11-52 


12-39 


13-27 


14-17 


10-67 


11-53 


12-40 


13-29 


14-19 


10-69 


11-54 


12-42 


13-30 


14-20 


10-7C 


11-56 


12-43 


13-32 


14-22 


10-72 


11-57 


12-45 


13-33 


14-23 


10-73 


11-59 


12-46 


13-35 


14-25 


10-74 


11-60 


12-48 


13-36 


14-26 


10-7€ 


11-62 


12-49 


13-38 


14-28 


10-77 


11-63 


12-51 


13-39 


14-29 


10-7S 


11-65 


12-52 


13-41 


14-31 


10-8C 


11-66 


12-53 


13-42 


14-32 


10-82 


11-67 


12-55 


13-44 


14-34 



chains. 

5514-34 
14-35 
14-37 
14-38 
14-40 
14-42 
14-43 
14-45 
14-46 
14-48 
14-49 
14-51 
14-52 
14-54 
14-55 
14-57 
14-58 
14-1 
14-61 
14-63 
14-64 
14-66 
14-67 
14-69 
14-70 
14-72 
14-73 
14-75 
14-76 
14-78 
14-79 
14-81 
14-82 
14-84 
14-86 
14-87 
14 

14-90 
14-92 
14-93 
14-95 
14-96 
14-98 
14-99 
15-01 
15-02 
15-04 
15-05 
15-07 
15-08 
15-10 
1511 
1513 
15-15 
1516 
15-18 
1519 
15-21 
15-22 
15-24 
15-25 



chains, 
5515-25 
15-27 
15-28 
15-30 
15-31 
15-33 
15-34 
15-36 
15-38 
15-39 
15-41 
15-42 
15-44 
15-45 
15-47 
15-48 
15-50 
15-51 
15-53 
15-54 
15-56 
15-57 
15-59 
15-61 
15-62 
15-64 
15-65 
15-67 
15-68 
15-70 
15-71 
15-73 
15-74 
15-76 
15-77 
15-79 
15-81 
15-82 
15-84 
15-85 
15-87 
15-88 
15-90 
15-91 
15-93 
15-94 
15-96 
15-98 
15-99 
16-01 
16-02 
16-04 
16-05 
16-07 
16-08 
16-10 
16-11 
16-13 
16-15 
16-16 
16-18 



370 380 / 



chains 

5516-18 

16-19 

16-21 

16 

16-24 
16-25 
16-27 
16' 
16-30 
16-32 
16-33 
16-35 
16-36 
16-38 
16-39 
16-41 
16-42 
16-44 
16-46 
16-47 
16-49 
16-50 
16-52 
16-53 
16-55 
16-56 
16-58 
16-60 
16-61 
16*63 
16-64 
16-66 
16-67 
16-69 
16-70 
16-72 
16-74 
16-75 
16-77 
16-78 
16-80 
16-81 
16-83 
16-84 
16-86 
16-88 
16-89 

16-yi 

16-92 
16-94 
16-95 
16-97 
16-98 
17-00 
17-02 
17-03 
17-05 
17-06 
17-08 
17-09 
17-H 



chains 
551711 
17-13 
17-14 
17-16 
17-17 
17-19 
17-20 
17-22 
17-23 
17-25 
17-27 
17-28 
17-30 
17-31 
17-33 
17-34 
17-36 
17-38 
17-39 
17-41 
17-42 
17-44 
17-45 
17-47 
17-49 
17-50 
17-52 
17-53 
17-55 
17-56 
17-58 



24 



TABLE I- 

Length of a Degrte of Latitude. 



' 39° 


40° 


410 


42° 


430 


440 


450 


46° 1 


470 


48° 


r \ 


chains. 


chains. 


chains. 


chains. 


:hains. 


chains. 


chains. 


chains. 


chains. 


chains. 


5518-05, 


5519-00 


5519-96 


5520-92 


5521-88 


5522-85 


5523-81 


5524-78 


5525-75 


5526-72 


> 


1 18-07 


19-02 


19-97 


20-93 


21-90 


22-86 


23-83 


24-80 


25-77 


26-73 


1 > 


2 18-08 


19-03 


19-99 


2095 


21-91 


22-88 


23-85 


24-82 


25-78 


26-75 


2 S 


3 1810 


19-05 


20-00 


20-96 


21-93 


22-89 


23-86 


24-83 


25-80 


20-76 


8 ) 


4 1811 


19-06 


20-02 


20-98 


21-94 


22-91 


23-88 


24-85 


25-82 


26-78 


4 \ 


5 1813 


19-08 


20-04 


21-00 


21-96 


22-93 


23-90 


24-86 


25-83 


26-80 


5 ( 


6 18-15 


19-10 


20-05 


21-01 


21-98 


22-94 


23-91 


24-88 


25-85 


26-81 


6 ( 


7 18-16 


1911 


20-07 


21*03 


21-99 


22-96 


23-93 


24-90 


25-86 


26-83 


7 I 


8 18-18 


1913 


20-08 


21-04 


22-01 


22-98 


23-94 


24-91 


25-88 


26-84 


8 I 


9 18-19 


1914 


20-10 


21-06 


22-02 


22-99 


23-9C 


24-93 


25-90 


26-86 


9 } 


10 18-21 


1916 


20-12 


21-08 


22-04 


23-01 


23-98 


24-94 


25-91 


26-88 10 ) 


11 18-22 


19-18 


20-13 


21-09 


22-06 


23-02 


23-99 


24-96 


25-93 


20-89>l > 


12 18-24 


19-19 


20-15 


2111 


22-07 


2304 


24-01 


24-98 


25-94 


26-91 12 ) 


13 18-26 


19-21 


20-16 


2112 


22-09 


23-06 


24-02 


24-99 


25-96 


26-92 13 \ 


14 18-27 


19-22 


20-18 


21-14 


2211 


23-07 


24-04 


25-01 


25-98 


26-94 14 ( 


15 18-29 


19-24 


20-20 


21-16 


22-12 


2309 


24-OC 


25-03 


25-99 


26-96 15 ( 


16 18-30 


19-25 


20-21 


2117 


22-14 


2310 


24-07 


25-04 


26-01 


26-9716 ( 


17 18-32 


19-27 


20-23 


2119 


22-15 


23-12 


24-09 


25-06 


26-02 


26-99 17 ( 


18 18-34 


19-29 


20-24 


21-20 


2217 


23-14 


2411 


25-07 


2604 


27-0018 <> 


19 18-35 


19-30 


20-26 


21-22 


22-19 


23-15 


24-12 


25-09 


26-06 


27-02'l9 > 


20 18-37 


19-32 


20-28 


21-24 


22-20 


23-17 


24-14 


2511 


26-07 


27-0420 ) 


21 18-38 


19-33 


20-29 


21-25 


22-22 


23-19 


24-15 


2512 


26-09 


27-05 21 ) 


22 18-40 


19-35 


20-31 


21-27 


22-23 


23-20 


2417 


2514 


26-10 


27-07(22 > 


23 18-41 


19-37 


20-32 


21-29 


22-25 


23-22 


2419 


2515 


26-12 


27-09 23 S 


24 18-43 


19-38 


20-34 


21-30 


22-27 


23-23 


24-20 


25-17 


26-14 


27-10 24 ) 


25 18-45 


19-40 


20-36 


21-32 


22-28 


23-25 


24-22 


25-19 


26-15 


27-12 25 ( 


26 18-46 


19-41 


20-37 


21-33 


22-30 


23-27 


24-23 


25-20 


26-17 


27-13|26 ( 


27 18-48 


19-43 


20-39 


21-35 


22-31 


23-28 


24-25 


25-22 


2619 


27-1527 ( 


28 18-49 


19-45 


20-40 


21-36 


22-33 


23-30 


24-27 


25-23 


20-20 


27-17 28 ( 


29 18-51 


19-46 


20-42 


21-38 


22-35 


23-31 


24-28 


25-25 


26-22 


27-18,29 ( 


30 18-53 


19-48 


20-44 


21-40 


22-36 


23-33 


24-30 


25-27 


26-23 


27-2030 ( 


31 18-54 


19-49 


20-45 


21-41 


22-38 


23-35 


24-32 


25-28 


20-25 


27-2131 I 


32 18-56 


19-51 


20-47 


21-43 


22-40 


23-36 


24-32 


25-30 


26-27 


27-2332 ( 


33 18-57 


19-53 


20-48 


21-45 


22-41 


23-38 


24-35 


25-32 


26-28 


27-2533 > 


34 18-59 


19-54 


20-50 


21-46 


22-43 


23-40 


24-36 


25-33 


26-30 


27-2634 ) 


35 18-60 


19-56 


20-52 


21-48 


22-44 


23-41 


24-38 


25-35 


26-31 


27-2835 ) 


36 18-62 


19-57 


20-53 


21-49 


22-46 


23-43 


21-46 


25-36 


26-33 


27-29'36 ) 


37 18-64 


19-59 


20-55 


21-51 


22-48 


23-44 


24-41 


25-38 


26-35 


27-31,37 ) 


38 18-65 


19-60 


20-56 


21-53 


22-49 


23-46 


24-43 


25-40 


26-36 


27-33 38 S 


39 18-67 


19-62 


20-58 


21-54 


22-51 


23-48 


24-44 


25-41 


26-38 


27-34 39 < 


40 18-68 


19-64 


20-60 


21-56 


22-52 


23-49 


24-46 


25-43 


26-39 


27-36 40 ( 


41 18-7C 


19-65 


20-61 


21-57 


2254 


23-51 


24-48 


25-44 


20-41 


27-3741 ( 


42 18-72 


19-67 


20-63 


21-59 


22-56 


23-52 


24-4S 


25-46 


26-43 


27-3942 ( 


43 18-72 


19-68 


20-64 


21-61 


22-57 


23-54 


24-51 


25-48 


26-44 


27-41 43 ( 


44 18-75 


19-7C 


20-6C 


21-62 


22-59 


23-56 


24-52 


25-49 


26-46 


27-42|44 ? 


45 18-76 


19-72 


20-68 


21-64 


22-60 


23-57 


24-54 


25-51 


26-47 


27-44 45 ) 


> 46 18-7* 


1 19-72 


20-61 


21-65 


2262 


23-59 


24-51 


25-52 


26-411 


27-4546 ) 


, 47 18-71 


1975 


20-7] 


21-67 


2264 


23-60 


24-57 


25-54 


26-51 


27-47 47 ) 


48 18-8] 


19-76 


20-72 


21 -6S 


22-65 


2362 


24-51 


25-56 


26-52 


27-49 48 ) 


49 18-81 


\ 19-78 


20-74 


21-7C 


22-67 


2364 


24-61 


25-57 


26-54 


27'5(M9 


50 18-84 


[ 19-8C 


) 20-76 


21-72 


22-61) 


23 65 


24-65 


\ 25-59 


26-56 


27-52.50 


51 18-8( 


; 19-81 


20- r 


21-74 


22-7C 


23-67 


24-64 


25-61 


26-57 


a7-53|51 ^ 


52 18-8T 


r 19-82 


\ 20-71 


2175 


22-72 


23-61) 


24-65 


> 25-62 


26- 51! 


27'55»a 


J 53 18-81 


> 19-84 


20-8( 


) 21-71 


22-72 


23-7C 


24-6' 


25-64 


26-6C 


27*57«3 j 


) 54 18-9] 


19-8( 


> 2081 


I 21-78 


22-75 


23-72 


24-61 


> 25-65 


26-62 


27*6864] 


) 55 18U* 


I 19-8* 


J 2084 


21 -8C 


22-77 


23-73 


24-7( 


) 25-67 


26-64 


27*80.66 I 


) 56 lH'J- 


I 19-81 


> 20- 8J 


> 21-85 


► 22-78 


23-75 


24-71 


I 25-61) 


26-65 


27-61)66 ; 


) 57 18-9 


> 19-9] 


208' 


r 21-81 


\ 22-8C 


23-77 


24-71 


J 25-7C 


26-67 


27*63UW ( 


) 5H 1H-D 


' 19-91 


\ 20-8( 


* 21-8! 


> 22-81 


23-78 


24-75 


> 25-72 


26-68 


27*66|68 J 


) 69 18-9 


i 19-94 


I 20-9( 


) 2186 


> 22-82 


23-8C 


24-7' 


f 25-73 


26-7C 


27-68W8 ) 


\ 601 19001 19-9( 


> 20-9' 


1 21-88 


il 22-85 


► 23-81 


24-7* 


) 25-75 


26-72 


1 27-68160 ) 



25 



t TABLE.1T. 
Length of a Degree of Longitude. 



29° 


30° 


31° 


32° | 
chains. 


33° 
chains 


34° 
chains. 


350 | 


36° 


37° 
chains. 


38° 


chains. 


chains. 


chains. 


chains. 


chains. 


chains. 


4843-17 


4795-32 


4747-01 


4696-75 


4645-06 


4591-96 


4537-45'4481-56 


4424-29 


4365-68 


42-40 


95-02 


46-19 


95-90 


44-19 


91-06 


36-53 


80-61 


23-33 


64-69 


41*02 


94-22 


45-36 


95-05 


43-32 


90-16 


35-61 


79-67 


22-36 


63-70 


40-84 


93-42 


44-53 


94-20 


42-44 


89-26 


34-69 


78-73 


21-40 


62-72 


40-06 


92-61 


43-71 


93-35 


41-57 


88-37 


33-77 


77-78 


20-43 


61-73 


39-28 


91-81 


42-88 


92-50 


40-69 


87-47 


32-84 


76-84 


19-46 


60-74 


38-50 


91-01 


42-05 


91-65 


39-82 


86-57 


31-92 


75-89 


18-49 


59-75 


37-72 


90*20 


41-22 


90-80 


38-94 


85-67 


31-00 


74-95 


17-53 


58-76 


30-94 


89*40 


40-39 


89-94 


38-06 


84-77 


30-08 


74-00 


16-56 


57-77 


36-16 


88-59 


39*56 


89-09 


37-19 


83-87 


29-15 


73-05 


15-59 


56-77 


35-38 


87-79 


38-73 


88-24 


36-31 


82-97 


28-23 


72-11 


14-62 


55-78 


34-00 


86-98 


37-90 


87-38 


35-43 


82-07 


27-30 


71-16 


13-65 


54-79 


33-82 


86-18 


37-07 


86-53 


34-55 


81-17 


26-38 


70-21 


12-68 


53-80 


33-04 


85-37 


36-24 


85-67 


33-68 


80-26 


25-46 


69-26 


11-71 


52-81 


32-26 


84-56 


35-41 


84-82 


32-80 


79-36 


24-53 


68-32 


10-74 


51-81 


31-47 


83-76 


34-58 


83-96 


31-92 


78-46 


23-60 


67-37 


09-77 


50-82 


30-09 


82-95 


33-75 


83-11 


31-04 


77-56 


22-68 


66*42 


08-80 


49-83 


29-01 


82-14 


32*92 


82-25 


30-16 


76-6E 


21-75 


65-47 


07-82 


48-83 


29-12 


81-33 


32-08 


81-40 


29-28 


75-7E 


20-83 


64-52 


06-85 


47-84 


28-34 


80-52 


31-25 


80-54 


28-40 


74-8£ 


19-90 


63-57 


05-88 


46-84 


27-55 


79-71 


30-42 


79-68 


27-52 


73-94 


18-97 


62-62 


04-91 


45-85 


26-77 


7S-90 


29-58 


78-82 


26-64 


73-04 


18-04 


61-67 


03-93 


44-85 


25-98 


78-09 


28-75 


77*97 


25*75 


72-1S 


17-11 


60*72 


02-96 


43-85 


25-20 


77-28 


27*92 


77-11 


24-87 


71-22 


16-19 


59-77 


01-98 


42-86 


24-41 


76-47 


27*08 


76*25 


23*99 


70-32 


15-26 


58-81 


01-01 


41-86 


23-62 


75-66 


26-25 


75*39 


23-11 


69-41 


14-33 


57-86 


00-04 


40-86 


22-83 


74-85 


25-41 


74-53 


22-22 


68-51 


13-40 


56-91 


4399-06 


39-87 


22-05 


74-04 


24-57 


73*67 


21-34 


67-6C 


12-47 


55-96 


98-08 


38-87 


21-26 


73-22 


23*74 


72-81 


20-45 


66-6S 


11-54 


55-00 


97-11 


37-87 


23-47 


72-41 


22-90 


71*95 


19*57 


65-76 


10-61 


54-05 


96-13 


36-87 


19-68 


71-60 


22-06 


71'09 


18-69 


64-86 


09-67 


53-09 


95-16 


35-87 


18-89 


70-78 


21-22 


70-22 


17*80 


63-97 


08-74 


52-14 


94-18 


34-87 


18-10 


69-97 


20-39 


69-36 


16-91 


63-06 


07-81 


51-19 


93-20 


33-87 


17-31 


69-16 


19-55 


68-50 


16-03 


62-1S 


00-88 


50-23 


92-22 


32-87 


16-52 


68-34 


18-71 


67*64 


1514 


61-24 


05-94 


49-27 


91-25 


31-87 


15-73 


67-53 


17*87 


66*77 


14-26 


60-33 


05-01 


48-32 


90-27 


30-87 


14-94 


66-71 


17-03 


65-91 


13-37 


59-42 


04-08 


47-36 


89-29 


29-87 


14-15 


65-89 


16-19 


65'05 


12-41, 


58-51 


03-14 


46-41 


88-31 


28-87 


13-35 


65-08 


15-35 


64-18 


11-59 


57-6C 


02-21 


4545 


87-33 


27-87 


12-56 


64-26 


14*51 


63*32 


10-70 


56-68 


01-28 


44*49 


86-35 


26-87 


11-77 


63-44 


13-67 


62-45 


09-81 


55-77 


00-34 


43-53 


85-37 


25-86 


10-98 


62-52 


12-82 


61-59 


08-93 


54-86 


4499-40 


42-57 


84-39 


24-86 


10-18 


61*81 


11-98 


60*72 


08-04 


53-9c 


98-47 


41-62 


83-41 


23-86 


09-39 


60-99 


11-14 


59'85 


07-15 


53-02 


97-53 


40*66 


82-42 


22-85 


08-59 


60-17 


1C30 


58*99 


06-26 


52-12 


96-59 


39-70 


81-44 


21-85 


07-80 


59-35 


09*45 


58*12 


05-36 


51-21 


95-66 


38-74 


80-46 


20-85 


07-00 


58-53 


08-61 


57'25 


04-47 


50-2£ 


94-72 


37-78 


79-48 


19-84 


06-21 


57-71 


07-76 


56-38 


03-58 


49-36 


93-78 


36-82 


78-49 


18-84 


05-41 


56-89 


06-92 


55'51 


02-69 


48-46 


92-84 


35-86 


77-51 


17-83 


04-61 


56-07 


06*07 


64*65 


01-80 


47-5£ 


91-91 


34-89 


76-53 


16-82 


03-82 


55*25 


05*23 


53*78 


00*90 


46-61 


90-97 


33-93 


75-54 


15-82 


03-02 


54-43 


04*33 


52*91 


00*01 


45-71 


90-03 


3297 


74-56 


14-81 


02-22 


53-6C 


03-54 


52-04 


4599-12 


44-8C 


89-09 


32-01 


73-57 


13-80 


01-42 


52-78 


02-69 


51'17 


98-22 


43-86 


88-15 


31-04 


72-59 


12-80 


00*62 


51-96 


01-84 


50-30 


97-33 


42-96 


87-21 


30*08 


71-60 


11-79 


4799-82 


51-13 


oi-oo 


49'42 


96-44 


42-04 


86-27 


29-12 


70-62 


10-78 


99-02 


50-31 


0015 


48-55 


95-54 


41-13 


85-32 


28-15 


69-63 


09-77 


98-22 


49-49 


4699-30 


47-68 


94-64 


40-21 


84-38 


27-19 


68-64 


08-76 


J 97-42 


48-6( 


98-45 


46-81 


93-75 


39-21 


83-44 


26-22 


67-66 


07-75 


1 96-6S 


47-84 


97-60 


45-94 


92-85 


38-37 


82-50 


25-26 


66-67 


06-74 


) 95-8S 


47-01 


96-75 


45-06 


91-96 


37-45 


81-56 


24-29 


65-68 


05-73 



26 



TABLE .jr. 
Length of a Degree of Longitude. 



, chains. 
3 4244*47 
43-4 
42-4} 
41-37 
40-34 
39-31 
38-27 
37-24 
3C-2C 
35-17 
34-13 
33-10 
32-OC 
31-02 
20-99 
28-95 
27-91 
26-87 
25-84 
24-80 
23-76 
22-72 
21-68 
20-64 
19-60 
18-56 
17-52 
16-48 
15-43 
14-39 
13-35 
12-31 
11-26 
10*22 
09-18 
08-13 
07-09 
06-04 
05-00 
03-95 
02-90 
01-86 
00-81 
6 4199-76 
98-72 
97-67 
96-62 
95-57 
94-52 
93-47 
92-42 
91-37 
90-32 
89-27 
88-22 
871 
8012 
85-07 
84-02 
82-96] 
81-911 



79-80 

78-75 

77 69 

70*04 

75-58 

74-52 

73-47 

72-41 

71-36 

70-30 

69-24 

68-18 

67-12 

66-07 

65-01 

63-95 

62-89 

61-83 

60-77 

59-71 

68-65 

67-58 

56-52 

55-46 

54-40 

53-44 

52-27 

51-21 

50-14 

49-08 

48-02 

46-95 

45-89 

44-82 

43-75 

42-69 

41-62 

40-55 

39-49 

38-42 

3735 

30-28 

3521 

34-14 

33-08 

3201 

30-93 

29-86 

28-79 

27-72 

26-Oii 

26*58 

94*51 

28*48 

22-36 

21*29 

20-21 

19.14 

18*06 



chains. 
4118-06 
16-99 
15-91 
14*84 
13*76 
12*69 
11*61 
10*53 
09*46 
08*38 
07-30 
00*22 
05-14 
04-0' 
02-9! 
01-91 

00*8; 

4099-75 
98-0' 
97-58 
96-50 
95-42 
94-34 
93-26 
92-17 
91-09 
90-01 
88-92 
87-84 
86-75 
85-67 
84-58 
83-50 
82-41 
81-33 
80-24 
79-15 
78-07 
76-98 
75- 
74-80 
73-71 
72-62 
71-53 
70-44 
69-35 
68-26 
67-17 
66-08 
64-99 
63-90 
62-81 
01-71 
60*62 
59*53 
58-43 
67-34 
56*26 
55*15 
54*06 



44° 



chains. 
4052*96 
51-87 
50*77 
49*67 
48-58 
47*48 
46-38 
45-28 
44*19 
43*09 
41-99 
40*89 
39 

38-69 
37-59 
36-49 
35*39 
34-29 
33-19 
32-09 
30-98 
29-88 
28-78 
27-67 
26*57 
25-47 
24-36 
23-26 
22-15 
21-05 
19-94 
18-84 
17-73 
16-62 
15-52 
14-41 
13-30 
12-19 
11 

09-98 
08-87 
07-76 
06-65 
05-54 
04-43 
03-32 
02-21 
01-10 
3999-98 
98-87 
97-76 
96-65 
95*58 
94-42 
93-31 
9219 
91*08 
89*96 

88-8; 
87-73 



52-961 86-62 



85*50 

84*38 

83*27 

82-15 

81-03 

79-91 

78*79 

77*68 

76-56 

75-44 

74-32 

73*20 

7: 

70-96 

69*84 

68-72 

67*59 

66-47 

65*35 

64-23 

63-11 

61-98 

60-86 

59-73 

58-61 

57-49 

66-36 

55-24 

54-11 

52-98 

51-86 

50-73 

49-60 

48-48 

47-35 

46-22 

45 

43-96 

42-83 

41-71 

40-58 

3945 

38-32 

37-18 

3605 

34-9: 

33-79 

32-C0 

31-53 

30 39 

29*26 

2813 

26*99 

26*86 

24-73 

23*59 

22-46 

21*32 

2019 

19-05 



47° 



17*91 

16*78 
15-64 
14*50 
13*36 
12-23 
11-09 
09-95 
08-81 
07*67 
06*53 
05-39 
04*25 
03-11 
01-97 
00-83 
3899-69 
98-54 
97-40 
96*26 
95*12 
93-97 
92*83 
91-68 
90-54 
89-40 
88-25 
87-11 
85-96 
84-81 
83-67 
82-52 
81-37 
80-23 
79-08 



49*12 

47*97 

46-81 

45*65 

44-50 

43-34 

42-18 

41-02 

39*86 

38*70 

37*54 

36-38 

35-22 

34-06 

32-90 

31-74 

30-58 

29-42 

28*26 

27*09 

25-93 

24*77 

23*60 

22*44 

21-28 

20-11 

18-95 

17-78 

16-62 

15-45 

14-29 

13-12 

11-95 

10-79 

09-62 



77-93 08-45 

76-78 07-28 

75-63 0611 

74-48 04-95 

73-34 03-78 

7219 02-61 

71-04 01-44 

69-89 00-27 
68-743799-10 

67-58 97-93 

66-43 96-76 

65 28 95-59 



64-13 

62-98 

61-82 

6067 

59-52 

58-36 

57-21 

56 06 

54-90 

53-7; 

52*59 

51-44 

50*28 



9441 

93-24 

92-07 

90-90 

89-72 

88' 

87-38 

8C-20 

85*08 

83-H0 

Bl'51 



79*1 

77*98 

76-80 

75-63 

74*45 

73*2' 

72*09 

70-92 

69-74 

68-56 

67-38 

66-20 

65-02 

63*84 

62-66 

61-48 

60-30 

59-12 

57-94 

56*76 

65*57 

64-39 

53-21 

52*02 

60*84 

49*66 

48*47 

47-29 

46-1C 

44-9S 

43-7C- 

42-55 

41-36 

40-18 

38-99 

37-80 

36-62 

35-4£ 

34-24 

330i 

31-86 

30-67 

29-48 

28-3f 

27-11 

25-92 

24-73 

23-53 

22-34 

211 

19*96 

18-77 

17-58 

16-38 

16*19 

14-00 

12*80 

11-61 

lo H 



chains. 
3709-22 

08-03 

06*83 

05-03 

04-44 

03-24 

02-05 

00-85 
3699*65 

98*46 ! 
97-2611 
96-06 llS 
94-86 12 ( 
93-66 13 ( 
92-46 14 ( 
91-26 15 ( 
90-061 
88*86 1 
87*66 1 
86*46 1 
85*26j2„> 
84*06 21 5 



- 



T ABLE* HI 



DIVERGENCY OP THE PaF.ALLEL OF LATITUDE AND THE 
PbIHE YeRTICAX. 



Dist 


| 28^ 


303 


32° 


34^ 


36^ ' 383 40 Q 42 Q I 44° 


| 460J 48° 


Dist; 


mile 


chns 


chns 


chns 


chns 


chns 


chns 


chns 


chns chns 


chns. 


chns. 


mile ) 


1 


0.01 


0.01 


0.01 


0.01 


0.91 


0.01 


0.01 


0.01 0.01 


0.01 


0.01 


1 ) 


2 


0.02 


0.02 


0.03 


0.03 


0.03 


0.03 


0.03 


0.04 | 0.04 


0.04 


0.04 


2 > 


3 


0.05 


0.05 


0.06 


0.06 


0.07 


0.07 


0.08 


0.08 


0.09 


0.09 


0.10 


3 ; 


4 


0.00 


0.09 


0.10 


0.11 


0.12 


0.13 


0.13 


0.14 


0.16 


0.17 


0.18 


4 ) 


5 


0.13 


0.14 


0.16 


0.17 


0.18 


0.20 


0.21 


0.23 


0-24 


0.26 


0.28 


5 


6 


0.19 


0.21 


0.23 


0.24 


0.26 


0.28 


0.30 


0.33 


0.35 


0.37 


0*40 


6 \ 


7 


0.26 


0.28 


0.31 


0.33 


0.36 


0.3S 


0,41 


0.44 


0.48 


0.51 


0.55 


7 ( 


8 


0.34 


0.37 


0.40 


0.43 


0.47 


0.50 


0.54 


0.58 


0.62 


0.67 


0.71 


8 ( 


9 


0.13 


0.47 


0.51 


0-55 


0.59 


0.64 


0.68 


0.73 


0.79 


0.84 


0.90 


9 


10 


0.53 


0.58 


0.63 


0.68 


0.73 


0.7S 


0.84 


0.90 


0.97 


1.04 


1.11 


10 


11 


0.65 


0.70 


0.76 


0.82 


0.88 


0.95 


1.02 


1.09 


1.17 


1.26 


1.35 


! 11 ( 


12 


0.77 


0.83 


0.90 


0.97 


1.05 


1.13 


1.21 


1.30 


1.40 


1.50 


1.61 


12 


13 


90 


0.98 


1.06 


1.14 


1.23 


1*33 


1.42 


1.53 


1.64 


1.76 


1.88 


13 ) 


14 


1.05 


1.14 


1.23 


1.33 


1.43 


1.54 


1.65 


1.77 


1.90 


2.04 


2.19 


1 14) 


15 


1.20 


1.30 


1.41 


1.52 


1.64 


1.76 


1.90 


2.03 


2.18 


2,34 


2.51 


15) 


16 


1.36 


1.48 


1.60 


1.73 


1.87 


2.01 


2.16 


2,32 


2.48 


2,66 


2.85 


16 


17 


1.54 


1.67 


1.81 


1.96 


2.11 


2.27 


2.44 


2.61 


2.80 


3.00 


3.22 


17 


18 


1.73 


1.88 


2,03 


2.19 


2.36 


2.54 


2.73 


2,93 


3.14 


3.37 


3.61 


18 ( 


19 


1.92 


2.09 


2.26 


2.44 


2.63 


2,83 


3.04 


3.26 


3. 50 


3.75 


4.03 


19 ( 


20 


2.13 


2.32 


2.51 


2.71 


2.92 


3-14 


3.37 


3.62 


3.88 


4.16 


4.46 


20 ( 


21 


2.35 


2.55 


2,76 


2.98 


3.22 


3,46 


3.72 


3.9v 


4.28 


4.59 


4.92 


21 ( 


22 


2.58 


2.80 


3.03 


3.28 


3.53 


3-80 


4.08 


4,38 


4.69 


5,03 


5.40 


22 1 


23 


2.82 


3.06 


3.32 


3.58 , 


3.86 


4.15 


4,46 


4.78 


5.13 


5.50 


5.90 


23 ) 


24 


3.07 


3.34 


3.61 


3-90 


4"20 


4.52 


4,85 


5.21 


5.59 


5.99 


6.42 


24 


25 


3.33 


3,62 


3.92 


4.23 


4.50 


4.90 


5.27 


5.65 


6.06 


6.50 


6.97 


25 ) 


26 


3.60 


3.91 


4.24 


4.57 


4.93 


5.30 


5.70 


6.11 6.56 


7.03 


7.54 


26 ) 


27 


3-89 


4.22 


4.57 


4.93: 


5-32 


5.72 


6.14 


6,59 7.07 


7.58 


8.13 


27 ) 


28 


4.18 


4.54 


4.91 


5-31 | 


5.72 


6.15 


6.61 


7.09 


7.60 


8.15 


8.74 


28 ) 


29 


4.48 


4.87 


5.27 


5.69| 


6.13 


6.60 


7.09 


7.61 


8.16 


8.74 


9.38 


29 > 


30 


4.80 


5.21 


5.64 


6.09! 


6.56 


7.06 


7.58 


8.14 


8,73 


9.36 


10.04 


30 ) 


31 


5.12 


5.57 


6.02 


6.50! 


7,01 


7.54 


8.10' 


8.69 


9.32 


9.99 


10.72 


31 ) 


32 


5.46 


5.93 


6.42 


6.93! 


7.47 


8.03 


8.63 


9.26 9.93 


10.66 


11.42 


32 ) 


33 


5.S1 


6.31 


6.83 


7.37 : 


7.94 


8.54 


9.18 


9.85 10.56 


11.32 


12.14 


33 \ 


34 


6.16 


e.eo 


7.25 


7.82 i 


8.43 


9.07 


9.74 


10.45 11.21 


12.02 


12.89 


34 ( 


35 


6.53 


7.09 


7.68' 


8.29 ' 


8-93 


9.61 


10.32 


11.08 11.88 


12.74 


13.66 


35 ( 


36 


6.91 


7.51 


8.12 


8.77 


9.45 


10.16 


10.92 


11.72 


12.57 


13.47 1 


14.45 


36 C 



Table showing the Dhlerence of Latitude and Departure in 
running SO chains, at any course from 1 to 60 minutes. 





Min's 


Links . 


Min's 


Links. 


Min's 


Links. 


Min's 


Links. 


Min's 
41 


Links. 


Min's 
51 


Links. 
119 


1 


2t 


11 


25| 


21 


49 


31 


72} 


95} 


2 


4f 


12 


28 


22 


51} 


32 


74f 


42 


98 


52 


121} 


3 


» 


13 


30} 


23 


53} 


33 


77 


43 


100* 


53 


123} 


4 


n 


14 


32} 


24 


56 


34 


79} 


44 


1021 


54 


126 


5 


hi 


15 


35 


25 


58} 


35 


81} 


45 


105. 


55 


128} 


6 


14 


16 


171 


26 


60} 


36 


84 


46 


107} 


56 


130} 


7 


164 


17 


39} 


27 


63 


37 


86} 


47 


109} 


57 


133 


8 


181. 


18 


42 


28 


65$ 
67} 


38 


881 


48 


112 


58 


135} 


9 


21 


19 


44} 


29 


39 1 


91 


49 


114} 


59 


137f 


10 


23| 


20 


46f 1 


30 | 


70 


40 


93} 


50 


116} 


60 


140 



28 



TABLES. 



Table for reducing Chains to Feet, and 
Feet to Chains. 



Chains 




Chains 




Chains 




Chains 




Chains 




or 


Feet. 


or 


Feet. 


or 


Feet. 


or 


Feet. 


or 


Feet. 


Links. 




Links. 


1386 


Links. 




Links. 




Links. 




1 


66 


21 


41 


2706 


61 


4020 


81 


5340 


2 


132 


22 


1452 


42 


2772 


62 


4092 


82 


5412 


3 


198 


23 


1518 


43 


2838 


63 


4158 


83 


5478 


4 


261 


24 


1584 


44 


2904 


64 


4224 


84 


5544 


5 


330 


25 


1650 


45 


2970 


65 


4290 


85 


5610 


6 


396 


26 


1716 


46 


3036 


G6 


4356 


86 


5676 


7 


462 


27 


1782 


47 


3102 


67 


4422 


87 


5742 


8 


528 


28 


1848 


48 


3168 


68 


4488 


88 


5808 


9 


594 


29 


1914 


49 


3234 


69 


4554 


89 


5874 


10 


660 


30 


1980 


50 


3300 


70 


4620 


90 


5940 


11 


726 


31 


2046 


51 


3366 


71 


4686 


91 


6006 


12 


792 


32 


2112 


52 


3432 


72 


4752 


92 


6072 


13 


858 


33 


2178 


53 


3498 


73 


4818 


93 


6138 


14 


924 


34 


2244 


54 


3564 


74 


4884 


94 


6204 


15 


990 


35 


2310 


55 


3630 


75 


4950 


95 


6270 


16 


1056 


36 


2376 


56 


3096 


76 


5016 


96 


6336 


17 


1122 


37 


2442 


57 


3762 


77 


5082 


97 


6402 


18 


1188 


38 


2508 


58 


3828 


78 


5148 


98 


6468 


19 


1254 


39 


2574 


59 


3894 


79 


5214 


99 


6534 


20 


1320 


40. 


2640 


60 


3960 


80 


5280 


100 


6600 



Table of Acres required per Mile, and per 100 Feet, 
for different widths. 



width. 


Acres 


Acres 


width. 


Acres 


Acres 


width. 


Acres 


Acres 


Feet. 


per 
Mile. 


per 

100 feet. 


Feet. 


per 
Mile. 


per 
100 feet. 


Feet. 


per 

Mile. 

5.45 


per 

100 feet. 


1 


.121 


.002 


23 


2.79 


.053 


45 


.103 


2 


.242 


.005 


24 


2.91 


.055 


46 


5.58 


.106 


3 


.364 


.007 


24* 


3.00 


.057 


47 


5.70 


.108 


4 


.485 


.009 


25 


3.03 


.058 


48 


5.82 


.110 


5 


•606 


.011 


26 


3.15 


.060 


49 


5.94 


.112 


6 


.727 


.014 


27 


3.27 


.062 


49 i 


6.00 


.114 


7 


.848 


.016 


28 


3.39 


.064 


50 


6.06 


.115 


8 


.970 


.018 


29 


3.52 


.067 


61 


6.18 


.117 


8f 


1.00 


.019 


30 


3.64 


.069 


52 


6.30 


.119 


9 


1.09 


.021 


31 


3.76 


.071 


53 


6.42 


.122 


10 


1.21 


.023 


32 


3.88 


.073 


54 


6.55 


.124 


11 


1.33 


.025 


33 


4.00 


.076 


55 


6.67 


.120 


12 


1.46 


.028 


34 


4.12 


.078 


56 


6.79 


.129 


13 


1.58 


.030 


35 


4.24 


.080 


57 


6.91 


.131 


14 


1.70 


.032 


36 


4.36 


.083 


57* 


7.00 


.133 


18 


1.82 


.034 


37 


4.48 


.085 


58 


7.03 


.134 


16 


1.94 


.037 


38 


4.61 


.087 


59 


7.15 


.186 


16* 


2.00 


.038 


39 


4.73 


.090 


60 


7.27 


.138 


17 


2.06 


.039 


40 


4.85 


.092 


61 


7.39 


.140 


18 


2.18 


.041 


41 


4.97 


.094 


62 


7.52 


.142 


19 


2.30 


.044 


41J- 


5.00 


.095 


63 


7.04 


.145 


20 


2.42 


.046 


42 


6.09 


.096 


64 


7.7<; 


.147 


21 


2.55 


.048 


43 


5.21 


.099 


65 


7.88 


.14'.) 


22 


2-67 


.051 


44 


5.33 


.101 


66 


8.00 


.151 



39 



MISCELLANEOUS. 



APPROXIMATE RULES CONVENIENT IN PRACTICE. 

I. Fob Correcting Random Lines.* 

1. Given the error of latitude or departure for any distance, to find 

the error of the course. 
Rule.— Three-sevenths of the error of latitude or departure, per mile, in links, 
will be the error of the course, in minutes. 

EXAMPLE. 
What is the error of the course for an error of 210 links of latitude or departure, 
in G miles? 

Here the error, per mile, is 35 links, three-sevenths of which is 15 minutes, the 
error required. 

2. Given the error of the course, to find the corresponding error of { 

latitude or departure for any distance. 

Rule Seven-thirds of the error of the course, in minutes, will be the error of ( 

latitude or departure, per mile, in links. 

EXAMPLE. 
What is the error of latitude or departure, in 6 miles, for an error of 15 minutes 
in the course? 

Here seven thirds of 15 is 35 links, the error per mile, or 210 links in C miles, the 
error required, 

II, For Running a Parallel or Latitude.! 
Given the distance run, east or west, on a great circle , to find the 
divergency from the parallel of latitude. 
Rule.— Multiply the square of the distance in miles, by the natural tangent of i 
the latitude, and the product will be the divergency, in links. 
EXAMPLE. 
After running £ miles, east or west, on the arc of a great circle, from latitude 38 
degrees, what will be the meridional distance south of the parallel? 
Here we have .731x62 — 2S links, the divergency required 

TRIGONOMETRICAL SERIES 

A3 A5 A7 

Sin A = A + + etc. 

2.3 2.3.4.5 2.3.4.5.6.7 

A2 A* A« 

Cos A = 1 + — -r etc. 

2 2.3.4 2.3.4.5.6 

A3 2A5 17A7 

Tan A = A + — 4- + + eto 

3 3.5 32.5.7 

1 A A3 2A5 

Cot A =- - — etc* 

A 3 32.5 33 5.7 

sin 3 A 3 sin 5 A 3.5 sin 7 A 

Arc A — sin A + + + — — + etc. 

2.3 2.4.5 2.4.6.7 

1 1 1 

Arc A — tan A tan 3 A + — tan 5 A tan 7 A + etc. 

3 5 7 



* This approximation is true to the nearest minute for all angles up to 3 deg. ; 
and to the nearest quarter of a degree for all angles up to 11 £ degrees. 

t This approximation may be considered practically correct for any distance net ' 
exceeding 30 miles. 



30 



MISCELLANK U S 



Rules for Solving all Cases of Plane Trigonometry. 

Case 1. 
Given all the Angles and One Side, to find the other Side. 
Rule. — As sine of the angle opposite the given side, is to sine of the angle 
opposite the required side, so is the given side to the required side. 

Case 2. 

Given two Sides and an Angle opposite one of them, to find the 

other Angles and Side. 

Rule. — As the side opposite the given angle, is to the other given side, so is sine 

of the angle opposite the former, to sine of the angle opposite the latter. 

>~<* ' r 

Case 3. 

Given two Sides and the included Angle , to find the other Angles 
and Side. 

Rule. — Subtract the given angle from 180 degrees and the remainder •will be the 
sum of the two unknown angles ; then say, as the sum of the two given sides is to 
their difference, so is tangent of half sum of unknown angles, to tangent of half 
their difference. Add this half difference of the unknown angles to their half sum 
for the angle opposite the greater side, and subtract it from the half sum ior the 
angle opposite the less side. 

Case 4. 
Given the Three Sides to find the Angles. 

Rule— Upon the longest side let fall a perpendicular from the opposite angle. 
This perpendicular will divide the base into two segments and the triangle into two 
right-angled triangles ; then say, as the given base is to the sum of the two other 
sides, so is the difference of those sides, to the difference of the segments of the 
base. To half the base add half the difference of the segments for the greater seg. 
ment, and subtract it from half the base for the less side ; then proceed as in Case 2 # 

Rule 2.— Add together the arith. comp. of the logarithms of the two sides, con- 
taining the requirea angle, the log. of the half sum of the three sides and the lng. 
of the difference of the half sum and the side opposite the required angle. The 
half sum of these four logarithms will be the logarithmic cosine of half the required 
angle. 



, For Finding the Diameter of a Tree. 
Ruie.— Annex a cipher to the number of links around the tree, and one fourth 
of the result will be the diameter, In inches. 

EXAMPLE. 

What is the diameter of a tree whose circumference is 10 links ? 

Here we have \ of 1G0 = 40 inches, the diameter required. 



TABLE FOR RUNNING ON SLOPES, 

In the following table the first column shows the angle, the second the number of 

links to be added to a chain on the slopes, to make 1 chain horizontal measurement. 



Angle. 


Cor. in links 




Cur. in links 


Anglo. 


Cor. in links 


Angle. 


Cor. in links 







o 




O 









4 


0.24 


11 


1.88 


18 


6.14 


2.', 


10.64 


5 




12 


'2.'2i 


19 


6.76 


26 


11.26 


G 


0.66 


13 


2.63 


20 


M2 


27 


12 .24 


7 


0.76 


11 


8.06 


21 


7.11 


28 


18.87 


8 


0.98 


16 




22 


7.85 


29 


14.84 





1.24 


10 


4.02 


2 5 


B.«4 


80 


1 ".. 1 7 


10 


1.65 


17 


4.66 


24 


9.47 


85 


22.07 



31 



TABLES. 

Position of the Principal Lines of the United States Surveys in the State of California , 

( MONTE DIABLO Merid,, Mt.Diablo. Lat, 37° 52' 47", Long. 121° 54' 49" W. 



Parallel. 


Latitude. 


Distance. 




o 


/ 


// 


Miles. 


Monte Diablo 


37 
38 


52 
18 


47 
53 





I Standard North 


30 


11 " » 


38 


44 


58 


60 


Ill " " 


39 


11 


4 


90 


IV »' " 


39 


37 


10 


120 


V " " 


40 


3 


15 


150 


VI " " 


40 


29 


21 


180 


VII " " 


40 


55 


26 


210 


vm •• " 


41 


21 


31 


240 


IX " " 


41 


47 


54 


270 


Oregon Boundary 


42 
37 




31 



54 


284 


I Standard South 


24 


11 " " ........ 


37 


11 


1 


48 


Ill " " 


36 


50 


8 


72 


IV " " 


36 


29 


14 


96 


V " ik 


36 


8 


21 


120 


VI " " 


35 


47 


28 


144 


VII " " 


35 


26 


35 


168 


VIII " " 


35 


5 


41 


192 


IX " " 


34 


41 


48 


216 


X " " 


34 


23 


55 


210 



Longitude 


Converg 


per Kange t 




o 


/ 


// 


Chains 








35.2 


0.00 





G 


37.5 


2.84 





6 


39.9 


2.88 





6 


42.4 


2.93 





6 


44.9 


2.97 





6 


47-5 


3.02 





6 


50.1 


2.06 





6 


52.8 


3.11 





6 


55.5 


8.16 





6 


58.3 


3.21 





6 


59.6 


1.48 





6 


33-4 


2.25 





6 


31.6 


2.22 





6 


23.8 


2.19 





6 


28.0 


2.17 





6 


26.3 


2.14 





6 


24-6 


2.11 





6 


22.9 


2.09 





G 


21.3 


2.C6 





G 


19.7 


2.03 





G 


18.1 


2.00 



HUMBOLDT MERID., Mt, Tierce, Lat, 40° 24' 56' ' , 


Long. 124° 07' 03" W. 


Parallel. 


Latitude, 


Distance, 


Longitude 
per Range. 


Converg. 


Mount Pierce 


o / // 
40 24 5G 

40 51 1 

41 17 6 

41 43 12 

42 

40 4 4 


Miles. 


30 

60 

90 
109.32 

24 


/ / // 

6 49.6 
6 52.3 
6 55.0 
6 57.9 
6 59.6 

6 47.5 


Chains. 
0.00 


1 Standard North 


3.09 


II " •• 


3.15 


Ill " " 


3.20 


Oregon Boundary 


2.09 


I Standard South 


Diverg, 
2.48 



SAN BERNARDINO Merid.. Mt.San Bern. Lat. 34° 07' 25", Long. 116°56' W. 



Parallel. 


Latitude. 


Distance. 


Longitude 
per Range. 


Converg. 


Mount San Bernardino 

1 Standard North 


o 
34 
34 
34 
35 
35 
36 
36 

33 
33 
33 
32 

32 


r 

7 
33 
59 
25 
51 
18 
44 

40 

25 

4 

43 

22 


// 
25 
32 
39 
4G 
53 

6 

31 
38 
34 
50 
56 


Miles. 



30 

60 

90 

120 

150 

180 

24 

48 

72 

96 

120 


o / // 

6 16.9 
6 18.8 
6 20.8 
6 22.8 
C 24.9 
6 27.1 
6 29.2 

6 15.3 
6 13.8 
6 12.3 
6 10.0 
6 9.5 


Chains. 
0.00 
2.47 


II " " 


2.51 


Ill * " 


2.56 , 


IV " » 


2.60 


V " «• 


2.64 ( 


VI " " 


2.68 < 


I Standard South 


Diverg, > 
1 95 ( 


11 '» 4V 


1 93 ) 


Ill " M 


1 90 ) 


IV *♦ " 

V » " 


J.87 5 
1.85 ) 



J23 



T A B L E S . 



Position of the Principal Lines of the United States Suhveys in tue 
STATE of NEVADA. 
The principal Base and Standard Parallels in this State are precisely the same 
as those of California. All the townships are numbered from the Monte Diablo 
meridian and baseline. The Fourth Standard Parallel base line commences at 
the California and Nevada State hues, run by A. \V. von Schmidt, at the line 
between Ranges 17 and 13, aud extends to the Utah boundary line, in 
Kange 70. 
There are four Guide Meridians, viz. : 
CARSON GUIDE MERIDIAN, running north from the Fourth Standard 

North, between Ranges 20 and 21 E. M. D. M. 
HUMBOLDT RIVER GUIDE MERIDIAN, running north from the Fourth 

Standard North, between ranges 35 and 36 E. M. D. M. 
REESE RIVER GUIDE MERIDIAN, running south from the Fourth Stan- 
dard North, between Ranges 42 and 43 E. M. D. M. 
T.UBY VALLEY GUIDE MERIDIAN, running N. and S. from the Fourth 
Standard Parallel North, between Ranges 55 and 56 of the Monte Diablo 
meridian. 



Position of the Principal Lines of the United States Surveys in 
UTAH TERRITORY. 
Initial Point, Salt Lake Base and Meridian. 

Latitude, 40° 46' 08" North; Longitude 111° 53' 47" West. 



Surveys North of the Base 


Line. 




Parallel. 


Latitude. 


Distanee, 


Longitude, 
per Range. 


Converge 


Initial Point 


o / // 

40 46 08 

41 07 00 
41 27 52 

41 48 44 

42 00 00 


Miles. 


24 
48 
72 
84.95 


o / // 
6 51.8 
6 53.9 
C 56.1 
6 58.4 
6 59.6 


Chains. 



I Standard North 

II M * 4 

ill »• " 

Oregon Line 


2.51 
2.54 
2.58 
1.40 



Surveys South of the Base Line. 



Initial Point 


40 

40 


46 
20 


IIS 


i Standard South 


03 


II " " 


39 


53 


57 


in M i - 


39 


27 


51 


IV " M . 


39 


(H 


46 


V M " . 


38 


36 


4U 


VI " " . 


38 


09 


■M 


All » '• . 


87 


43 


2fl 


VIU 


37 


17 


22 


Arizona Line 


37 


00 


00 



Miles. 


30 

60 

90 
120 
150 
180 
210 
240 



51.8 
49.1 
45.6 
44.0 
41.5 
39.1 
36.7 
34.3 
32.1 

30.1 



Chains 

3.09 
8105 
2.99 
2.95 
2.91 
2.80 

2.78 



COLORADO BASE LINE, 

Latitude of Initial Point, 33 deg. 51 mln. ; Longitude, 114 dog. 29 ndn. 

Meridian runs north 12 miles to Lat. 34 deg. 1 min. 27 see. 

Convergeiuy, 0,97 



a:j 



TABLES 



Position oft»e Peixctpal Lines oe the U. S. Suet, if ARIZONA TER, 

Initial Point, junct. of Salt & Gila rivers. Lat. 33° 22' 57", Long. 112° 15' 46" 

Surveys north of Gila and Salt Elver Base Line. 



Parallel. 



Initial Point 

I Standard North. 
II " " . 

III « " . 

IV -' " . 
V » . 

VI " " . 

VII " " . 

V11I »• " . 

IX " " . 

X " " . 

North Boundary 



Latitude. 



o / // - 

33 22 57 

33 43 51 

34 04 45 
34 25 38 

34 46 32 

35 07 25 
35 28 18 

35 49 12 

36 10 05 
36 30 58 

36 51 52 

37 00 00 



Distance. 


Longitu de 
per Range. 


Converg. 


iriles. 


o 


/ // 


Chains. 








6 13.6 





24 





6 15.1 


1.92 


48 





6 16.6 


1.95 


72 





6 18.2 


1.97 


96 





6 19.8 


2.00 


120 





6 21.4 


2.02 


144 





6 23.0 


2.05 


168 





6 24.7 


2.08 


192 





6 26.4 


2.10 


216 





6 28.1 


2.13 


240 





6 29.9 


2.16 


249.35 





6 30.6 


0.85 



Surveys south of Gila and Salt Rh 


er Base Line. 






° ' " Miles o / // 


Chains. 


Initial Point 


33 22 57 
32 56 50 



30 


6 13.6 
6 11.8 





I Standard South 


2-37 


II " " 


32 30 42 


60 


6 10.0 


2.33 


Ill " " 


32 04 35 


90 


6 8.2 


2.29 


IV " " 


31 38 27 


120 


6 6.5 


2.26 



Initial Point of TVilliametta Meridian, WASHINGTON TERRITORY. 
Base Line, Lat. 45° 31 ' 13" North, Long. 122° 30' 26' > W. 









Longitude 
per Range. 




Parallel. 


Latitude. 


Distance. 


Converg. 




o / // 


Mlies. 


o / // 


Chains. 


Initial Point 


45 31 13 
45 52 04 



24 


7 25.0 
7 27.7 





I Standard North 


2.96 


11 " " 


46 12 55 


48 


7 30.6 


3.00 


Ill " " 


46 33 46 


72 


7 33.4 


3.04 


IV " " 


46 54 37 


96 


7 36.3 


3.07 


V " " 


47 15 28 


120 


7 39.3 


3.11 


VI " " 


47 36 19 


144 


7 42.4 


3.15 


VII " " 


47 57 09 


168 


7 45.4 


3.19 


VIII " " 


48 18 00 


192 


7 48.6 


3.23 


IX »* " 


48 38 51 


216 


7 51.8 


3.27 


X " " 


48 59 41 


240 


7 55.1 


3.30 



Position of the Principal Lines of the U.S. Surveys in MONTANA TER. 
Initial Point, intersec.prin. base& mer„ lat.45°46'27N.; Long. 111°27'14"W 



Parallel. 


Latitude. 




o 


/ // 


Principal Base 


45 
46 


46 27 


1 Standard North 


07 15 


11 " " 


46 


28 03 


Ill " " 


46 


48 51 


IV " " 


47 


09 39 


V " " 


47 


30 27 


VI " " 


47 


51 15 


VII » * 


48 


12 03 


I Standard Souih 


45 


20 27 


II " " 


44 


54 27 



. 


Longitude 




Distance 


per Range. 


Converg. 


Miles. 


o 


/ 


// 


Chains. 








7 


27.8 





24 





7 


28.2 


3.01 


48 





7 


28.5 


3.03 


72 





7 


28.8 


3.06 


96 





7 


29.2 


3.11 


120 





7 


29.6 


3.15 


144 





7 


29.9 


3.19 


168 





7 


30.3 


3.22 
Diverg. 


30 





7 


27.3 


3.71 


60 





7 


27.8 


3.67 



34 



T A B L E S , 



POSITION OF THE PlUNCIPAL LlNES OR THE U. S. SURVEYS IN TUE 

STATE OF OREGON. 
Initial Point, intersection of Willamette meridian and base line, 

Lat. 45° 31' 13" North; Long. 122° 30' 2C" Wc 



Surveys north of the Willamette Base Line. 



Parallel. 


Latitude. 


Distance 

Miles. 



24 

42 


Longitude 
per Range. 

o / // 
7 25.0 
7 27.7 
7 29.8 


Convcrg. 


Willamette Base Line 

I Standard North 

11 " M ... 


o / // 
45 31 13 

45 52 04 

46 07 42 


Chains. 

2.90 
2.25 



Surveys south of the Willamette Base Line. 



Willar 


nette Base Line,.... 


45 


31 


13 


1 Standard South 


45 


05 


09 


II 


" 


44 ,. 


44 


39 


05 


in 


41 


i« 


44 


23 


26 


IV 


44 


u 


43 


57 


22 


V 


44 


44 


43 


30 


30 


VI 


4 * 


44 


43 


10 


20 


VII 


44 


44 


42 


44 


21 


VIII 


44 


44 


42 


28 


42 


IX 


*• 


'* 


42 


07 


50 


North 


Bound. 


of Calif a.. 


42 


00 


00 



Mlies. 


30 

60 

78 
108 
132 
162 
192 
210 
234 
243 



// 
25.0 
21.6 
18.3 
16.3 
13.1 
10.6 
07.7 
04.0 
02.8 
00.4 
59.5 



Chains. 

3.62 
3.59 
2.15 
3.51 
2.76 
3.41 
3.38 
2,00 
2.63 
0.99 



ACKNOWLEDGEMENTS. 



In the Compilation of this little work I am indebted for information to 
Honorable THEOD. WAGNER.... U.S. Surveyor-Gen'l for California. 

41 Nevada. 



£. S. DAVIS ♦' 

FRED'K SALOMAN... 4I 

JOHN WASSON '• 

WM. MeMICKEN 44 

R. II. MASON " 



44 Utah Ter. 
44 Arizona Ter. 
44 Washington T 
41 Montana Ter 



And herewith I tender my sincere thanks for the interest which the above named 
U.S. Surveyor-Generals have taken in furnishing me so promptly with the required 
notes of the different principal Initial Points of the United States Public 
Land Survey on this Coast. 



Very respectfully, 



w. schmol:'.. 



35 



TABLES. 



TABLES OF GRADES, 

Per Mile and per 100 Feet, measured horizontally and corresponding to different 
Angles of Elevation. 







Feet 


Feet 




Feet 


Feet 




Feet 


Feet 




Feet 


Feet 






per 


per 




per 


per 




per 


per 




per 


per 


o 


/ 


mile. 
1. 


100 ft. 


o / 


mile. 


100 ft.- 


o / 


mile. 
54. 


100 ft. 


o r 


mile. 


1C0 ft. 






0.01894 


18 


27.64 


0.5237 




1.02273 




81. 


1.53409 





1 


1.536 


0.02091 




28. 


0.53030 




55. 


1.04167 


53 


81.40 


1.5419 






2. 


0.03788 




29. 


0.54924 


36 


55.30 


1.0472 




82. 


1.55303 






3. 


0.05682 


19 


29.17 


0.5528 




56. 


1.06061 


54 


82.94 


1.5710 





2 


3.072 


0.0582 




30. 


0.56818 


37 


56.83 


1.0763 




83. 


1.57197 






4. 


3.0757f 


20 


30.72 


0.5818 




57. 


1.07955 




84. 


1.59091 





3 


4.608 


0.0873 




31. 


0.58712 




58. 


1.09848 


55 


84.47 


1.6000 






5. 


0.09470 




32. 


0.60606 


38 


58.37 


1.1054 




85. 


1.60985 






6. 


0.11364 


21 


32.26 


0.6109 




59. 


1.11742 




86. 


1.62879 





4 


6.144 


0.1164 




33. 


0.62500 


39 


59.90 


1.1S45 


56 


86.01 


1.6291 






7. 


3.13258 


22 


33.80 


0.6400 




60. 


1.13636 




87. 


1.64773 





g 


7.680 


0.1455 




34. 


0.64394 




61. 


1.15530 


57 


87.54 


1.6583 






8. 


0.15152 




35. 


0.66288 


40 


61.44 


1.1636 




88. 


1.66666 






9. 


0.17045 


23 


35.33 


0.6691 




62. 


1.17424 




89. 


1.68561 





6 


9.216 


0.1746 




36. 


0.68182 


41 


62.97 


1.1927 


58 


89.08 


1.6873 






10. 


0.18939 


24 


36.86 


0.6982 




63. 


1.19318 




90. 


1.70455 





7 


10.75 


0.2037 




37. 


0.70076 




64. 


1.21212 


59 


90.62 


17164 






11. 


0.20833 




J8. 


3.71970 


42 


64.51 


1.2218 




9L 


1.72348 






12. 


0.22727 


25 


38.40 


0.7273 




65. 


1.23106 




92. 


1.74242 





8 


12.29 


0.2328 




39. 


0.73864 




66. 


1.25000 


1 


92.16 


1.7455 






13. 


0.24621 


26 


39.94 


0.7564 


43 


66.04 


1.2509 




93. 


1.76136 





9 


13.82 


0.2619 




40. 


0.75758 




67. 


1.26894 




94. 


1.78030< 






14. 


0.26515 




41. 


3.77652 


44 


67.57 


1.2800 




95. 


1.79924 ( 






15. 


0.28409 


27 


41.47 


0.7855 




68. 


1.28788 


1 2 


95.23 


1.8038 ( 


10 


15.36 


0.2909 




42. 


0.79545 




69. 


1.30682 




96. 


1.81818< 






16. 


0.30303 




43. 


0.81439 


45 


69.11 


1.3090 




97. 


1.83712< 


11 


16.90 


0.3200 


28 


43.01 


0.8146 




70. 


1.32576 




98. 


1.85606( 






17. 


0.32197 




44. 


0.83333 


46 


70.64 


1.3381 


1 4 


98.30 


1.8620 ( 






18. 


0.31091 


29. 


44.54 


0.8436 




71. 


1.34470 




99. 


1.87500? 


12 


18.43 


3.3491 




15. 


0.85227 




72. 


1.36364 




100. 


1.89394) 






19. 


3.35985 




i6. 


).87121 


47 


72.18 


1.3672 




101. 


1.91288) 


13 


19.96 


0.3782 


30 


16.08 


0.8727 




73. 


1.38258 


1 06 


101.4 


1.9202 ) 






20. 


0.37879 




47. 


0.89015 


48 


73.72 


1.3963 




102. 


1.93182) 






21. 


0,39773 


31 


47.62 


0.9018 




74. 


1.40152 




103. 


1.95076) 


14 


21.50 


0.4073 




48. 


0.90U09 




75. 


1.42045 




104. 


1.96969) 






22, 


0.41667 




49. 


0.92803 


49 


75.26 


1.4254 




147. 


2.78409S 






23. 


0.43561 


32 


49.16 


0.9309 




76. 


1.43939 


1 36 


147.4 


2.7932 ( 


15 


23.01 


0.4364 




50. 


0.94697 


50 


76.80 


1.4545 




148. 


2.80303C 






24. 


0.45155 


33 


30.69 


0.9600 




77. 


1.45833 




149. 


2.82197C 


16 


24.58 


0.4055 




51. 


0.96591 




78. 


1.47727 




150. 


2.84091C 






25. 


0.47348 




52. ' 


0.98485 


51 


78.33 


1.4837 


1 38 


150.5 


2.8514 ( 






26. 


0.49242 


34 


52.23 


0.9891 




79. 


1.49621 




151. 


2.85985/ 


17 


26.11 


0.494G 




33. 


1.00379 


52 


79.87 


1.5128 




152. 


2.87879? 






27. 


0.51136 


35 


53.76 


1.0182 • 




30. 


1.51515 


1 40 


L53.6 


2.9097 ( 



30 



T A J* L E . 



TABLE OF 
RADII, MIDDLE ORDINATES, &c, OF CURVES. 

Chokd 100 Fjeet. 
jy Tlie Tangential Angle is always one-half of the Angle of Deflection. 



Angle 


Radii 


Deflec. 


Tang. 


Mid. 


Angle 
of 


Radii 


Deflec. 


Tang. 


Mid, 


of 


in feet. 


distance, 


dist. 


Ordln. 


in feet. 


dist. 


dist. 


Ordin. 


Deflec. 




in ft. 


in feet. 




Deflec. 




in feet. 


in feet. 




o / 










o / 










1 


343775 


.029 


.014 


.004 


2 6 


2729 ' 


3.665 


1.832 


.458 ( 


2 


171887 


.058 


.029 


.008 


■■ 12 


2604 


3.839 


1.919 


.480 ( 


4 


85944 


.116 


.058 


.014 


" 18 


2491 


4.014 


2.007 


.502 < 


G 


57296 


.174 


.087 


.022 


" 24 


2387 


4.188 


2.094 


.523 ( 


8 


42972 


.232 


.110 


.028 


" 30 


2292 


4.363 


2.182 


.545 ( 


10 


34378 


.291 


.145 


.036 


"36 


2204 


4.538 


2.209 


.507 ( 


12 


28648 


.349 


.174 


.043 


"42 


2122 


4.712 


2.350 


.589 ( 


14 


24556 


.407 


.203 


.050 


"48 


2046 


4.886 


2.443 


.011 ( 


16 


21485 


.405 


.232 


.058 


" 54 


1976 


5.060 


2.530 


.032 ( 


18 


19098 


.523 


.201 


.065 


3 


1910 


5.235 


2.018 


.054 ( 


20 


17189 


.581 


.290 


.073 


" 15 


1763 


5.GGG 


2.8CG 


.710 < 


22 


15627 


.G39 


.319 


.080 


" 30 


1637 


0.108 


3.054 


.764 ( 


24 


14324 


.097 


.348 


.087 


" 45 


1528 


0.544 


3.272 


.818 < 


26 


13222 


.756 


.378 


.095 


4 


1433 . 


0.980 


3.490 


.873 ( 


28 


12278 


.814 


.407 


.102 


« 15 


1348 


7.416 


3.708 


.927 < 


30 


11459 


.872 


.430 


.109 


» 30 


1274 


7.853 


3.927 


.981 ( 


32 


10743 


.930 


.4G5 


.116 


" 45 


1207 


8.289 


4.145 


1.030 ( 


34 


10111 


.988 


.494 


.123 


5 


1140 


8.722 


4.3G1 


1.091 < 


36 


9549 


1.040 


.523 


.131 


" 15 


1092 


9.159 


4.579 


1.14G < 


38 


9046 


1.104 


.552 


.138 


" 30 


1042 


9.595 


4.798 


1.200 < 


40 


8594 


1.102 


.581 


.145 


" 45 


990.8 


10.03 


5.015 


1.255 ( 


42 


8185 


1.221 


.010 


.152 


6 


955.4 


10.47 


5.235 


1.309 < 


44 


7814 


1.279 


.039 


.159 


" 15 


917.0 


10.90 


5.450 


1.3G4 < 


46 


7474 


1.337 


.GG8 


.167 


" 30 


882.0 


11-34 


5.G70 


1.419 < 


48 


7162 


1.395 


.097 


.174 


" 45 


849.3 


11-78 


5.890 


1.473 ( 


50 


6876 


1.453 


,72G 


.182 


7 


819.0 


12.21 


6.105 


1.528 < 


52 


6611 


1.511 


.755 


.189 


» 15 


790.8 


12.G4 


6.320 


1.582 ( 


54 


6367 


1.509 


.784 


.197 


" 30 


7G4.5 


13.08 


6.540 


1.037 ( 


56 


6139 


1.027 


.813 


.204 


" 45 


739.9 


13.51 


6.755 


1.692 ( 


58 


5928 


1.085 


.842 


.211 


8 


716.8 


13.95 


6.975 


1.746 I 


1 


5730 


1.745 


.872 


.218 


" 15 


695.1 


14.38 


7.190 


1.801 < 


ii 4 


5372 


1.800 


.930 


.232 


" 30 


674.6 


14.81 


7.405 


1.855 ( 


" 8 


5056 


1.976 


.988 


.246 


" 45 


G55.5 


15.25 


7.025 


1.910 ( 


" 12 


4775 


2.094 


1 1.047 


.201 


9 


637.3 


15.08 


7.840 


1.9G5 < 


" 10 


4524 


2.210 


: 1.105 


.275 


" 15 


620.2 


10.12 


8.0G0 


2.019 < 


» 20 


4298 


2.320 


; i.io3 


.290 


" 30 


603.8 


1G.55 


8.275 


2.074 


•i 24 


4093 


2.443 


i 1.221 


.306 


" 45 


588.4 


1G.99 


8.495 


2.123 < 


«« 28 


3907 


2.669 


: 1.279 


.320 


10 


573.7 


17.43 


8.715 


2.183 < 


" 32 


3737 


2.G7G 


i 1.338 


.334 


" 15 


559.7 


17.87 


8.936 


2.238 < 


" 36 


3581 


2.793 


! 1.39G 


.349 


» 30 


546.4 


18.30 


9.150 


2.292 


" 40 


34;]8 


2.908 


i 1.454 


.304 


" 45 


533.8 


18.73 


9.305 


2.347 < 


«■ 44 


8306 


3.026 


I 1.512 


.378 


11 


521.7 


19.17 


9386 


2*401 


; «• 48 


3183 


3.141 


: . 1.570 


.393 


" 15 


510.1 


19.61 


9.806 


2.466 


•• 52 


3009 




: 1.029 


.407 


" 30 


499.1 


20.05 


10.03 


2.511 


" 56 


2964 


3374 


1.681 


.422 


" 45 


188.5 


20.50 


10.25 


2.666 < 


2 


2865 


3.490 


! 1.745 


.436 


12 


■ 47H.3 


20.94 


1 U7 


2.620 



37 



TABLE. 

TEMPERATURE OF BOILING WATER 

Corresponding to the Height of Barometer and Altitude above Sea Level, 



not*. 


Baro. 


Alti. 




inch. 


feo' , 





16.79 


15221 


2 


16.86 


15112 


4 


16.93 


15003 


6 


17.00 


14895 


8 


17.08 


14772 


D 


17.16 


14649 


2 


17.23 


14543 


4 


17.31 


14421 


6 


17.38 


14315 


8 


17.46 


14195 


) 


17.54 


14075 


2 


17.62 


13956 


4 


17.70 


13837 


6 


17.78 


13718 


8 


17.86 


13601 


] 


17.93 


13498 


2 


18.00 


13396 


4 


18.08 


13280 


6 


18.16 


13164 


8 


18.24 


13049 





18.32 


12934 


2 


18.40 


12820 


4 


18.48 


12706 


G 


18.56 


12593 


8 


18.64 


12480 





18.72 


12367 


2 


18.80 


12256 


4 


18.88 


12144 


6 


18.96 


12033 


8 


19.04 


11923 





19.13 


11799 


2 


19.21 


11690 


4 


19.29 


11581 


G 


19.37 


11472 


8 


19.45 


11364 





19.54 


11243 


o 


19.62 


11136 


4 


19.70 


11029 


G 


19.78 


10923 


8 


19.87 


10804 





19.96 


10685 


o 


20.05 


10567 


4 


20.14 


10450 


6 


20.22 


10346 


8 


20.31 


10230 





20.39 


10127 


2 


20.48 


10011 


4 


20.57 


9896 


6 


20.65 


9794 


8 


20.73 


9693 



Deg. 

194.0 



195.0 
.2 
.4 
.6 



196.0 
.2 
.4 



197.0 



198.0 



199.0 



200.0 
.2 
.4 
.6 



201.0 
.2 

.4 
.6 



202.0 
.2 
.4 
.6 
•8 

203.0 
•2 
.4 

.6 



inch. 
20.82 
20.91 
21.00 

21.09 
21.18 

21.26 
21.35 
21.44 
21.53 
21-62 

21.71 
21.81 
21.90 
• 21*99 
22.08 

22.17 
22.27 
22.36 
22.45 
22.54 

22.64 
22.74 
22.84 
22.93 
23.02 

23.11 

23.21 
2P.31 

23-40 

23.40 

23.59 
2\69 
2:\79 
23.89 
23.98 

24.03 
24.18 
24.28 
24.38 
24.48 

24.58 
24.68 
24.78 
24.88 
24.98 



25.03 
25.18 
25.28 
25.38 
25.43 



ox 



1 Alti. 


Thermo. 


! feet. 


Deg. 


9579 


204.0 


' 9466 


.2 


; 9353 


.4 


! 9241 


.6 


j 9130 


.8 


9031 


205.0 : 


8920 


.2 


8810 


.4 


8700 


.6 


8590 


.8 


8481 


206.0 


8361 


t 2 


8253 


A 


8145 


•6 


8038 


• 8 : 


7932 


207.0 ; 


7814 





7708 


A 


7602 


.6 


7498 


.8 


7381 


208.0 


7266 


.2 


7151 • 


.4 


7048 


.6 


6945 


.8 ; 


6843 


209.0 


6729 


,0 


6617 


A 


6516 


.6 


6415 


.8 


6304 


210.0 


6193 


,2 


6082 


!I 


5972 


.6 


5874 


.8 


57C4 


211.0 


5656 


.2 


5547 


.4 


5440 


.6 


5332 


.8 


5225 


212.0 


5119 


below 


5013 


.2 


4907 


.4 


4802 


.6 




.8 


4697 




4593 


213.0 


4489 


.2 


4386 


.4 


4272 


.6 



Baro. 

inch. 
25.59 
25.70 
25.88 
25.91 
26.01 

26.11 
26.22 
26.33 
26.43 
26.54 

26.64 
26.75 
26.86 
26.97 
27.08 

27.18 
27.29 
27.40 
27.51 
27.62 

27.73 
27.84 
27.95 
28.06 
28.17 

28-29 
28-40 
28.51 
28.62 

28.73 

28.85 
28.97 
29.09 
29.20 
29.31 

29.42 
29.54 
29.65 
29.77 



30.00 sea level. 1 

se i level. 
30.12 - lo4 
30.24 
30.35 
30*47 



30.59 
30.71 
30.82 
30.93 



38 



T A B L E. 



THERMOMETERS. 



Corresponding Temperatures by the Fahrenheit , Centigrade 
and Reaumur Scales. 



Fahren. 


Centi. 


Reau. 


Fahren. 


Centi. 


Reau. 


Fahren. 


Centi. 


Reau. 


Deg. 


Deg. 


Dog. 


Dig. 


Deg. 


Deg. 


Deg. 


1 Deg. 


Deg. 


212 


100.0 


80.0 


128 


53.3 


42.6 


44 


6.7 


5.3 


210 


98.9 


79.1 


126. 


52.2 


41.7 


42 


5.5 


4.4 


208 


97.8 


78.2 


124 


51.1 


40.8 


40 


4.4 


3.5 


206 


96.7 


77.3 


122 


50.0 


40.0 


38 


3.3 


2.6 


201 


95.6 


7G.4 


120 


48.9 


39.1 


36 


2.2 


1.7 


202 


94.4 


75.5 


118 


47.8 


38.2 


34 


1.1 


0.8 


aoo 


93.3 


74.6 


116 


46.7 


37.3 


32 


0.0 


.0 


108 


92.2 


73.7 


114 


45.6 


36.4 


30 


- 1.1 


-0.8 


106 


91.1 


72.9 


112 


44.4 


35.5 


28 


2.2 


1.7 


194 


90.0 


72.0 


110 


43.3 


34.6 


26 


3.3 


2.G 


192 


88.9 


n.i 


108 


42.2 


33.7 


24 


4.4 


3.5 


190 


87.8 


7C.2 


106 


41.1 


32.8 


22 


5.5 


4.4 


188 


86.7 


69.3 


104 


40.0 


32.0 


20 


- 6.7 


- 5.3 


186 


85.6 


68.4 


102 


38.9 


31.1 


18 


7.7 


6.1 


184 


84.4 


67.5 


100 


37.8 


30.2 


16 


8.9 


7.3 


182 


83.3 


66.6 


98 


36.7 


29.3 


14 


10.0 


8.0 


180 


82.2 


65.7 


96 


35.6 


28.4 


12 


11.1 


8.8 


178 


81.1 


64.9 


94 


34.4 


27.5 


10 


12.2 


9.7 


176 


80.0 


64.0 


92 


33.3 


2G.G 


8 


- 13.3 


-10.6 


174 


78.9 


63.1 


90 


32.2 


25.7 


6 


14.4 


11.5 


172 


77.8 


62.2 


88 


31.1 


24.8 


4 


15.5 


12.4 


170 


76.7 


61.3 


86 


30.0 


24.0 


2 


16.7 


13.2 


167 


75.0 


60.0 


84 


28.9 


23.1 


- 


17.7 


14.1 


166 


74.4 


59.5 


82 


27.7 


22.1 


2 


18.9 


15.1 


104 


73.3 


58.6 


80 


2G.6 


21.2 


- 4 


- 20.0 


-16.0 


162 


72.2 


57.7 


78 


25.5 


20.4 


6 


21.1 


16.8 


160 


71.1 


56.8 


77 


25.0 


20.0 


8 


22.2 


17.7 


158 


70-0 


56.0 


74 


23.3 


18.6 


10 


23.3 


18.6 


15G 


68.9 


5'.1 


72 


22.2 


17.7 


12 


24.4 


19.5 


154 


67.8 


54.2 


70 


21.1 


16.8 


14 


25.5 


20.4 


152 


66.7 


53.3 


68 


20.0 


1G.0 


10 


- 2G.7 


-21.2 


150 


G5.6 


52 .4 


66 


18,9 


15.1 


18 


27.7 


22.1 


148 


64.4 


51.fi 


64 


17.7 


14.1 


20 


28.9 


28.1 


14G 


63.3 


50.6 


62 


16.6 


13.2 


22 


30.0 


24.0 


144 


52.2 


49.7 


60 


15.5 


12.4 


24 


31.1 


24.8 


142 


Gl.l 


48.8 


58 


14.4 


11.5 


26 


32.2 


25.7 


140 


60.0 


48.0 


50 


13.3 


10.0 


- 28 


- 33.3 


-26.6 


138 


58.9 


47.1 


54 


}->:2 


9.7 


30 


84,4 


'-•7.-, 


136 


57.8 


46.9 


52 


11.1 


8.8 


32 


354 




134 


56.7 


46.3 


50 


10.0 


8.0 


34 


56.7 


29.3 


132 


55. G 


4 1.4 


48 


8.9 


7.3 


30 


r.7.8 


30.2 


130 


51.4 


i '•.'> 


46 


7.7 


G.l 


38 


38.9 


31.1 



39 



TABLES. 



Equivalents of Lineai Measures, 



S Inches. 


Links. 


Feet 


Varas. | Yards. 


ChaiDS. 


Miles. 


Sp'Lea. 
0.000006 


EngXea. 


i 


9.126263 


0.083333 


0.029965-0.027778 


0.001263 


0.000016 


0.000005 ( 


/7.92 


1 


0.66 


0.237325 0.22 


0.01 


0.000125 


0.000047 


0.000042 ( 


)12 


1.515152 


1 


0.359583: 0.333333 


0.015152 


0.000189 


0.000072 


0.000063 ( 


> 33.372 


1.213636 


2.781 


1 10.927 


0.042136 


0.000527 


0.0002 


0.000176 , 


)36 


4.545455 


3 


1.0787491 1 


0.045455 


0.000568 


0.000216 


0.000189 , 


)792 


100 


66 


23.73247(22 


1 


0.0125 


0.004746 0.004167 v 


',63360 
(166860 


8000 


5280 


1898.598 1760 


80 


1 


0.379720 0.333333 


21068.18 


13905 


5000 4635 


210.6818 


2.633523 


1 1 0.877841 


( 190380 


24000 


15840 


5695.793)5280 


240 


3 


1.139159 


1 



Equivalents of Square Measures, 



Varas. 



0.859329 
) 1.16369865 1 

563.230148 '484 
\ 5632.30148 '4840 
\3604672.95 3097600 



Chains. 



V25000000 
(a 



32442056.5 



21483225 
! 27878400 



0.00177547 
0.00206612 

1 
10 

6400 

44386.8285 
57600 



0.00017755 
0.00020661 
0.1 

1 
640 

4438.68285 
5760 



Miles. 



Sp. League 



Eng. Lea.) 



0.00000028 0.00000004 
0.03000032 0.00000005 
0.00015625 0.00002253 



0.0015625 

1 

6.93544195 
9 



0.00022533 
0.14418692 

1 
1.29768226 



'0.00000003; 
! 0.00000004) 
0.00001736 ) 
0.00017361 ) 
0.11111111) 
0.77060466 ) 
1 



French Units of Weights and Measures, &c. 



Metre. 



\ Measures of Length. 
/Myriametre. . . .10000 meters 

(Kilometre 1000 " 

.Hectometre .... 100 " 
/Dekametre..... 10 '* 

)Metre 1 " 

(Decimetre... one-tenth M 
\Centimetre... one 100th " 
(Millimetre.. one 1000th " 
)l Kilometre . . . .3230.833 feet 
<Jl Hectometre. ...323.033 feet 

Measure of Surface. 

([Hectare 10000 Sq. Meters 

NHectare 2.471 acres 

(Are 119.6 Sq. Yard s 



Gramme* 



Weights. 

Millier 1000000 Grammes 

Quintal.... 100000 ■« 

Myriagram' 10000 * l 

Kilogram'.. 1000 " 

Hectogram ' 100 " 

Dekagram'. 10 " 

Gramme... 1 " 

Decigram'. one-tenth " 

Centigram, one 100th " 

Milligram'. one 1000th M 



Cubic Weight. 
1 Cubic M.. .2204.6 lbs. A.D. 
1 Cub. Litre, 2.2046 " " 
j Tonneau.. 1000000 gr'mmes 



Litre. 



Measures of Volume. ( 

Kilolitre 1000 litres) 

Hectolitre 100 

Decalitre... 10 

Litre 1 

Decilitre ....one-tenth 
Centillitre. . . .one 100th 
Millilitre.... one 1000th 
1 Fluid Dr'm.,0,0036967 
1F1. Ounce... 0.0295739 
1F1. Found. 0.35483656 



Cubic Measure. 
1 Cub.M. . .264.17 wine gal. (J 
1 Cub. Litre. 1.0567 wine gal. 
t Cub.Millilitre 0.0151 grainsC 



40 



TABLES. 




Equivalents Lineal Measures. 



Links. 


Feet. 


Yards. 


0.120263 


0.083333 


0.027778 


1 


0.66 


0.22 


1.515152 


1 


0.333333 


4.515155 


3 


1 


100 


OG 


22 


8000 


5280 


17G0 


4.9710591 


3.280899 


1.093G33 



Chains. 

0.001 2G3 
0.01 

0.015152 
0.045455 

1 
80 
0.0497106 



Miles. 

0.000016 
0.000125 
0.000189 
0.000568 
0.0125 
1 
0.0OOC213 



Meters. 

0.02540005 
0.201 16839 
0.3048006 
0.9144018 
20.1168396 
1609.347168 
1 



Equivalents of Square Measures. 



Inches. 

1 
{144 
/1296 
Z627264 
>6272640 
) 1550.0589477 



Feet. 

0.0069444 

1 
9 

4356 
4356G 
10.7612982 



Yards. 

0.0007716 
0.333333 

1 
484 
4840 
1.1960331 



Chains. 



0.0000016 
0.0002296 
10.00206612 

1 
10 
0.0024711 



Acres. 

0.00000016 
0.0000229 
0-00020661 
0.1 

1 
0.00024711 



Meters. 

0.000645161 
0.092903184 
0.836128656 
404.671063 
4046.71063 
1 



Equivalents of Weights. 



Grains, 


Scruples. 


Drachms, 


Oz. Troy. 


Oz. A.D. 


P'd Troy. 


.P'd A.D. 


1 


0.05 


0.0166G6 


0.002083 


0.002285 


0.000173 


0.000142 


20 


1 


0.333333 


0.041066 


0.045714 


0.003472 


0.002857 


60 


3 


1 


0.125 


0.139215 


0.010416 


0.008571 


480 


24 


8 


1 


0.990295 


0.083333 


0.0685702 


437.5* 


21.875 


7.18311 


1.0098 


1 


0.075941 


0.0625 


5760 


288 


96.00 


12 


13.168 


1 


0.822857 


7000 


350 


116.66 


14.5833 


16 


1.215278 


1 


15.43316 


0.771658 


0.257219 


0.032151 


0.035275 


0.002679 


0.002203 



Grammes( 

0.648004 J 
1.296008 
3.888024 ( 
31.10419 ) 
28.35017 < 
373.2502 ( 
453.6028 ( 
1 



Equivalents of Liquid Measures. 



Gills. 



)4 

) 8 
S32 

(8.4524 



0.25 

1 
|2 

8 
'2.1131 



Quarts. 

0.125 
0.50 

1 
4 
1.05656 



Gallons. 

0.03125 

0.125 

0.25 

1 
0.2641407 



Liters. 

0.1182955 
0.4737821 
0.94G3G42 
3.7854579 
1 



Cubic Inches,) 

7.21875 

28.875 

57.75 

231. 

61.0105 



A standard avoirdupois pound is the weight of 27.7015 cubic inches of distilled 
water, weighed in air at a temperature of 30 . 8-3 Fahrenheit, barometer at 30 inches. 
A cubic inch of such water weighs 252.G037 grains. 

A cubic foot contains 7.48068 gallons liquid measure. A gallon is equal to a 
cylinder of 7 inches In diameter and 6 inches high. 



41 



TABLES. 



United States Gold Coins, 





Standard Weight. 


Deviation 
Allowed. 


Least 


Denomination 


Grains. 


Troy Ounces. 


Current 
Weight. 


1 Double Eagle 

1 Eagle 

1 Half Eagle . . 
1 Three Dollar. 
1 Quarter Eagle 
1 Dollar 


516.00 

258.00 

129.00 

77.40 

64.50 

25.80 


1.075000 
0.537500 
0.268750 
0.161250 
0.134375 
0.053750 


0.5 Grains. 
0.5 
0.25 " 

0.25 ** 
0.25 t{ 
0.25 " 


513.42 Grains 

256.71 

128.36 
77.02 " 
64.18 " 
25.67 



United States Silver Coins. 



) Denomination. 


Standard Weight. 


Deviation ) 


Grains. 


Troy Ounces. 


Allowed. / 


) 1 Trade Dollar 


420.00 

412.50 

192.90 

96.45 


0.8750000 
0.8593750 
0.4018750 
0.2009375 
0.0803750 
0.0401875 


1 5 Grains. ; 


) 1 Dollar 


15 " ) 


\ 1 Half Dollar 


15" ) 


( 1 Quarter Dollar 


1.0 s i 


( 1 Dime 


38.58 
19.29 


0.5 " ( 


( 1 Half Dime 


0.5 " ) 



United States Standard Weight for 
GOLD AND SILVER COINS. 



Gold Coins. 



> 20,000. 
) 15,000. 

; 10,000. 

5,000. 
2,500. 
1,000. 



Troy 
Ounces. 



1075.000 
806.250 
537.500 
208.750 
1*54.375 
5\750 



Trade Dollars. 



1,000. 
750. 
500. 
250. 
100. 
50. 



Troy 
Ounces. 

875^00~ 
65f«.25 
437.50 
218.75 
87.50 
4?.75 



Silver Dollars. 



1 000. 
'750. 
500. 
250. 
100. 




Subsidiary 
Coins. 



1,000 
500 
250 
100 
50 
10 



Troy 
Ounces. 

803.7500 
401.8750 | 
200.9375 , 
80.3750 
40.1875 
8.0375 



U2 granos 

( 3 tomincs . . 
^ 2 adarmes.. 
' S ochavas . . 

) 8 onzas 

\ 2 marcos . . . 



Mexican Weights. 



1 tomin Equal. 

1 adarrue 

1 ochava or dracrna " 

lonza " 

1 marco 

1 libra " ■ 



9.2 grains Troy. 

27.7 grains " 

55.5 grains " 

443 . 8 grains or 0,9245 oz. Troy, i 

3550.5 grains or 7,396 oz. Troy., 

7101. grains or 14,7937 oz. Troy. 



42 



T A B r. E 
Of valve of One Ounce troy, of different fineness. 



GOLD. 



Fine. 


Dols. Cts. 


Fine. 


Dols. Cts. 





00.00 


463 


9 50.90 


1 


02.07 


470 


9 71.58 


2 


04-13 


480 


9 92.25 


3 


0G.20 


490 


10 12.92 


4 


08.27 


500 


10 33.59 


5 


10.34 


510 


10 54.26 


G 


12.40 


520 


10 74.94 


7 


14.47 


530 


10 95.61 


8 


10.54 


540 


11 16.28 


9 


18.60 


550 


11 36.95 


10 


20.67 


560 


11 57.62 


20 


41.34 


570 


11 78.29 


30 


62.02 


580 


11 98.97 


40 


82.69 


590 


12 19.64 


50 


1 03.36 


600 


12 40.31 


GO 


1 24.03 


610 


12 60.98 


70 


1 44.70 


620 


12 81.65 


80 


1 65.37 


630 


13 02.33 


90 


1 86.05 


640 


13 23.00 


100 


2 06.72 


650 


13 43.67 


110 


2 27.39 


660 


13 64.34 


120 


2 48.06 


670 


13 85.01 


130 


2 68.73 


680 


14 05.08 


140 


2 89.41 


690 


14 2G-30 


150 


3 10.08 


700 


14 47.03 


1G0 


3 30.75 


710 


14 67.70 


170 


3 51.42 


720 


14 88.37 


180 


3 27.09 


730 


15 09.04 


190 


3 92.76 


740 


15 29.72 


203 


4 13.44 


750 


15 50.39 


210 


4 34.11 


760 


15 71.06 


220 


4 54.78 


770 


15 91.73 


230 


4 75.45 


780 


16 12.40 


240 


4 96.12 


790 


16 33.07 


250 


5 16.80 


800 


16 53.75 


2G0 


5 37.47 


810 


16 74.42 


270 


5 58.14 


820 


16 95.09 


280 


5 78.81 


830 


17 15.76 


290 


5 99.48 


840 


17 36.43 


300 


20.1C 


850 


17 57.11 


310 


6 40.83 


860 


17 77.78 


320 


6 61.50 


870 


17 98.45 


330 


6 82.17 


880 


18 19.12 


340 


7 02.84 


890 


18 39.79 


86Q 


7 23-51 


900 


18 60.46 


. 3G0 


7 44.19 


910 


18 81.14 


' 370 


7 64.86 


920 


19 01.81 ! 


380 


7 85.53 


930 


19 22.48 


> 390 


8 06.20 


940 


19 43.15 


) 400 


8 26.87 


950 


19 63.82 


) 410 


8 47.53 


960 


13 84.50 


) 420 


8 68.23 


970 


20 05.17 ' 


) 430 


8 8H.8J 


980 




) 440 


9 09.5G 


090 




450 


j 30.2J 









SILVER. 




Fine. 


Dols. Cts, 


Fine. 


Dola. Cts. 





00.00 


400 


59.47 


1 


03.13 


470 


60.77 


2 


00.26 


480 


02.06 


3 


03.39 


490 


6 1.36 


4 


1.52 


500 


64.65 


5 


09.65 


510 


65.94 


G 


00.78 


520 




7 


09.90 


530 


68*53 


8 


01.03 


540 


09.82 


9 


01.10 


550 


71.11 


10 


01.29 


560 


72.40 


20 


02.59 


570 


73.69 


30 


03.88 


580 


74.99 


40 


05.17 


590 


70.28 


50 


06.46 


600 


77.58 


60 


07.76 


610 


78.87 


70 


09.05 


620 


80.16 


80 


10.34 


630 


81.45 


90 


11.04 


640 


82.75 


100 


12.93 


650 


84.04 


110 


14.22 


660 


85.33 


120 


15.52 


670 


86.63 


130 


16.81 


680 


87.92 


140 


18.10 


690 


89.21 


150 


19.39 


700 


90.51 


160 


20.69 


710 


91.80 


170 


21.98 


720 


93.09 


180 


23.27 


730 


94.38 


190 


24.57 


740 


95.68 


200 


25.86 


750 


96.97 


210 


27.15 


760 


98.26 


220 


28.44 


770 


99.56 


230 


29.74 


780 


1 09.85 


240 


31.03 


790 


1 02.14 


250 


32.32 


800 


1 03.43 


260 


33.62 


810 


1 04.72 


270 


34.91 


820 


1 00.02 


280 


36.20 


830 


1 07.31 


290 


37.49 


840 


1 08.01 


300 


38.79 


850 


1 09.90 


310 


40.08 


860 


1 11.10 


320 


41.37 


870 


1 12.48 


330 


42.67 


880 


1 13.78 


340 


43.96 


890 


1 15.07 


350 


45.25 


900 


1 16.36 


360 


46.55 


910 


1 17.00 


370 


47.84 


920 


1 18195 


380 


4'.». 13 


930 


1 2 ».2 1 


390 


50.42 


940 


1 21.51 


400 


51.72 


950 


l 22.8 ; 


410 


53. 1 


960 


1 21.12 


420 




970 




430 


55.6 i 


ti 










i a -. i 








1 20.20 



43 




A CARD. 



Sib: 

Should you desire to have a 
Solar Reflector attached to your transit 
instrument, the eye-piece cap and the 
object-glass cap must be forwarded to me. 
Before taking the eye-piece cap off from 
the eye-piece, please screw it on tight, 

) and scratch a perpendicular lino with a 

) knife over the front face of the cap, and 

) mark the top of the line with a cross, as 

? shown in the annexed engraving. 

S The price of a Solar Reflector is $20.00. 

For the last thirty years the undersigned has been established 
in San Francisco ; and in that long period of time became person- 
ally acquainted with hundreds of surveyors and engineers. A few 
in that large number will criticise the invention, and may not 
feel inclined to use the new method till they are moro familiar 
with the motion of our globe, and fully understand and study the 
astronomical fundamental law, and get acquainted with the prin- 
ciple by which the Reflector produces an'accurate result. The 
more enlightened class of surveyors will readily appreciate the 
inversion after a short examination — and they will have the ben- 
efit of getting a good night's rest after their hard day's work, as | 
no observation of Polaris will be necessary to establish the 
meridian. Besides, by establishing the true meridian in day- 
time, and directly on the line of their survey, instead of doing it , 
in camp (which may be several miles distant from the field of 
operation), they will have the assurance of more correct work. 

This plain and entirely mechanical apparatus, which solves a 
complicated astronomical problem so readily and easily, will be 
in general use in a few years. Those using the Reflector will 
give the inventor due credit for spending six years of his life to 
bring this invention to perfection; besides six months more in 
publishing the little book, and making daily observations with 
the Reflector, whenever the weather was favorable, to test the 
correctness of the tables. 

* + * Repairs of every description of Surveying instruments exe- 
cuted in a workmanlike manner, at moderate charges, by 

Yours respectfully, 



w m. s c h m o l z, 

Surveying-Instrument Maker, 

420* Montgomery Street, S. F. 



44 



019 423 967 1 



■H 









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mm 
HI HBHHBHlG 

H Maul! 
■HHH 

■■ HPESS 

BHi HHflnSl 



LIBRARY OF CONGRESS 



019 423 967 1 i 



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